I have an Acer Switch 10 with a 32-bit UEFI. I installed 32-bit UEFI GRUB and was able to boot 64-bit Ubuntu. It definitely was not 32-bit Ubuntu - I was specifically using a 64-bit installer/LiveCD.
I can confirm definitively that a machine with 32-bit firmware can absolutely boot a 64-bit operating system.
I have an Acer Switch 10 with a 32-bit UEFI. I installed 32-bit UEFI GRUB and was able to boot 64-bit Ubuntu. It definitely was not 32-bit Ubuntu - I was specifically using a 64-bit installer/LiveCD.
I can confirm definitively that a machine with 32-bit firmware can absolutely boot a 64-bit operating system.