I tried to boot with acpi_backlight=vendor which didn't help; now there aren'd any backlights registered in /sys/class/backlight at all.

This is an HP ProBook 6560b as well:

$ lspci -v
00:00.0 Host bridge: Intel Corporation 2nd Generation Core Processor Family DRAM Controller (rev 09)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, fast devsel, latency 0
        Capabilities: <access denied>

00:01.0 PCI bridge: Intel Corporation Xeon E3-1200/2nd Generation Core Processor Family PCI Express Root Port (rev 09) (prog-if 00 [Normal decode])
        Flags: bus master, fast devsel, latency 0
        Bus: primary=00, secondary=01, subordinate=01, sec-latency=0
        I/O behind bridge: 00002000-00002fff
        Memory behind bridge: d0300000-d03fffff
        Prefetchable memory behind bridge: 00000000c0000000-00000000cfffffff
        Capabilities: <access denied>
        Kernel driver in use: pcieport
        Kernel modules: shpchp

00:16.0 Communication controller: Intel Corporation 6 Series/C200 Series Chipset Family MEI Controller #1 (rev 04)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, fast devsel, latency 0, IRQ 48
        Memory at d0424000 (64-bit, non-prefetchable) [size=16]
        Capabilities: <access denied>                                                                                                                                                           
        Kernel driver in use: mei                                                                                                                                                               
        Kernel modules: mei                                                                                                                                                                     
                                                                                                                                                                                                
00:19.0 Ethernet controller: Intel Corporation 82579V Gigabit Network Connection (rev 04)                                                                                                       
        Subsystem: Hewlett-Packard Company Device 1619                                                                                                                                          
        Flags: bus master, fast devsel, latency 0, IRQ 46                                                                                                                                       
        Memory at d0400000 (32-bit, non-prefetchable) [size=128K]                                                                                                                               
        Memory at d042a000 (32-bit, non-prefetchable) [size=4K]                                                                                                                                 
        I/O ports at 3020 [size=32]                                                                                                                                                             
        Capabilities: <access denied>                                                                                                                                                           
        Kernel driver in use: e1000e                                                                                                                                                            
        Kernel modules: e1000e                                                                                                                                                                  
                                                                                                                                                                                                
00:1a.0 USB controller: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #2 (rev 04) (prog-if 20 [EHCI])                                                      
        Subsystem: Hewlett-Packard Company Device 1619                                                                                                                                          
        Flags: bus master, medium devsel, latency 0, IRQ 16                                                                                                                                     
        Memory at d0429000 (32-bit, non-prefetchable) [size=1K]                                                                                                                                 
        Capabilities: <access denied>                                                                                                                                                           
        Kernel driver in use: ehci_hcd                                                                                                                                                          

00:1b.0 Audio device: Intel Corporation 6 Series/C200 Series Chipset Family High Definition Audio Controller (rev 04)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, fast devsel, latency 0, IRQ 49
        Memory at d0420000 (64-bit, non-prefetchable) [size=16K]
        Capabilities: <access denied>
        Kernel driver in use: snd_hda_intel
        Kernel modules: snd-hda-intel

00:1c.0 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 1 (rev b4) (prog-if 00 [Normal decode])
        Flags: bus master, fast devsel, latency 0
        Bus: primary=00, secondary=02, subordinate=02, sec-latency=0
        Memory behind bridge: d0200000-d02fffff
        Capabilities: <access denied>
        Kernel driver in use: pcieport
        Kernel modules: shpchp

00:1c.2 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 3 (rev b4) (prog-if 00 [Normal decode])
        Flags: bus master, fast devsel, latency 0
        Bus: primary=00, secondary=03, subordinate=03, sec-latency=0
        Memory behind bridge: d0100000-d01fffff
        Prefetchable memory behind bridge: 00000000d0600000-00000000d06fffff
        Capabilities: <access denied>
        Kernel driver in use: pcieport
        Kernel modules: shpchp

00:1c.3 PCI bridge: Intel Corporation 6 Series/C200 Series Chipset Family PCI Express Root Port 4 (rev b4) (prog-if 00 [Normal decode])
        Flags: bus master, fast devsel, latency 0
        Bus: primary=00, secondary=04, subordinate=04, sec-latency=0
        Memory behind bridge: d0000000-d00fffff
        Capabilities: <access denied>
        Kernel driver in use: pcieport
        Kernel modules: shpchp

00:1d.0 USB controller: Intel Corporation 6 Series/C200 Series Chipset Family USB Enhanced Host Controller #1 (rev 04) (prog-if 20 [EHCI])
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, medium devsel, latency 0, IRQ 16
        Memory at d0428000 (32-bit, non-prefetchable) [size=1K]
        Capabilities: <access denied>
        Kernel driver in use: ehci_hcd

00:1f.0 ISA bridge: Intel Corporation HM65 Express Chipset Family LPC Controller (rev 04)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, medium devsel, latency 0
        Capabilities: <access denied>
        Kernel modules: iTCO_wdt

00:1f.2 SATA controller: Intel Corporation 6 Series/C200 Series Chipset Family 6 port SATA AHCI Controller (rev 04) (prog-if 01 [AHCI 1.0])
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, 66MHz, medium devsel, latency 0, IRQ 45
        I/O ports at 3048 [size=8]
        I/O ports at 3054 [size=4]
        I/O ports at 3040 [size=8]
        I/O ports at 3050 [size=4]
        I/O ports at 3000 [size=32]
        Memory at d0427000 (32-bit, non-prefetchable) [size=2K]
        Capabilities: <access denied>
        Kernel driver in use: ahci

01:00.0 VGA compatible controller: Advanced Micro Devices [AMD] nee ATI Seymour [Radeon HD 6400M Series] (prog-if 00 [VGA controller])
        Subsystem: Hewlett-Packard Company Device 161b
        Flags: bus master, fast devsel, latency 0, IRQ 47
        Memory at c0000000 (64-bit, prefetchable) [size=256M]
        Memory at d0300000 (64-bit, non-prefetchable) [size=128K]
        I/O ports at 2000 [size=256]
        Expansion ROM at d0340000 [disabled] [size=128K]
        Capabilities: <access denied>
        Kernel driver in use: radeon
        Kernel modules: radeon

01:00.1 Audio device: Advanced Micro Devices [AMD] nee ATI Caicos HDMI Audio [Radeon HD 6400 Series]
        Subsystem: Hewlett-Packard Company Device 161b
        Flags: bus master, fast devsel, latency 0, IRQ 50
        Memory at d0320000 (64-bit, non-prefetchable) [size=16K]
        Capabilities: <access denied>
        Kernel driver in use: snd_hda_intel
        Kernel modules: snd-hda-intel

03:00.0 System peripheral: JMicron Technology Corp. SD/MMC Host Controller (rev 30)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: bus master, fast devsel, latency 0, IRQ 18
        Memory at d0104000 (32-bit, non-prefetchable) [size=256]
        Expansion ROM at d0600000 [disabled] [size=64K]
        Capabilities: <access denied>
        Kernel driver in use: sdhci-pci
        Kernel modules: sdhci-pci

03:00.2 SD Host controller: JMicron Technology Corp. Standard SD Host Controller (rev 30) (prog-if 01)
        Subsystem: Hewlett-Packard Company Device 1619
        Flags: fast devsel, IRQ 18
        Memory at d0103000 (32-bit, non-prefetchable) [size=256]
        Capabilities: <access denied>
        Kernel modules: sdhci-pci

04:00.0 Network controller: Broadcom Corporation BCM4313 802.11b/g/n Wireless LAN Controller (rev 01)
        Subsystem: Hewlett-Packard Company Device 145c
        Flags: bus master, fast devsel, latency 0, IRQ 19
        Memory at d0000000 (64-bit, non-prefetchable) [size=16K]
        Capabilities: <access denied>
        Kernel driver in use: brcmsmac
        Kernel modules: bcma, brcmsmac