Comment 7 for bug 1554099

I'm pretty sure this is the source of the problem, software-properties looks at Apt configuration options, which are the following in a fresh install of Xenial.

bdmurray@clean-xenial-amd64:~$ grep -r "APT::Periodic" /etc/apt/*
/etc/apt/apt.conf.d/10periodic:APT::Periodic::Update-Package-Lists "1";
/etc/apt/apt.conf.d/10periodic:APT::Periodic::Download-Upgradeable-Packages "0";
/etc/apt/apt.conf.d/10periodic:APT::Periodic::AutocleanInterval "0";
/etc/apt/apt.conf.d/20auto-upgrades:APT::Periodic::Update-Package-Lists "1";
/etc/apt/apt.conf.d/20auto-upgrades:APT::Periodic::Unattended-Upgrade "1";

So we have autodownload set to 0, and unattended set to 1. Looking at the code in SoftwareProperties.py we see:

147 if apt_pkg.config.find_i(softwareproperties.CONF_MAP["autoupdate"]) > 0:
148 # Autodownload
149 if apt_pkg.config.find_i(softwareproperties.CONF_MAP["unattended"]) == 1\
150 and apt_pkg.config.find_i(softwareproperties.CONF_MAP["autodownload"]) == 1 :
151 return softwareproperties.UPDATE_INST_SEC
152 elif apt_pkg.config.find_i(softwareproperties.CONF_MAP["autodownload"]) == 1 and \
153 apt_pkg.config.find_i(softwareproperties.CONF_MAP["unattended"]) == 0:
154 return softwareproperties.UPDATE_DOWNLOAD
155 elif apt_pkg.config.find_i(softwareproperties.CONF_MAP["unattended"]) == 0 and \
156 apt_pkg.config.find_i(softwareproperties.CONF_MAP["autodownload"]) == 0:
157 return softwareproperties.UPDATE_NOTIFY
158 else:
159 return None

So somebody's created a situation we hadn't planned on.