The XT-286 is an AT class machine and therefore the keyboard (also AT class) won't work on a 5160, unless the keyboard is an auto-switching type.
Forgive me but I believe you're quite wrong about this. The XT-286 is indeed an XT class. The keyboard is autoswitching anywho and I've tested it on numerous XT machines in the past (and it does work on my 5160).
See this sentence from wikipedia:
"In 1986, the XT/286 (IBM 5162) with a 6 MHz Intel 80286 processor was introduced. This system actually turned out to be faster than the ATs of the time using 8 MHz 286 processors due to the fact that it had zero wait state RAM that could move data more quickly."
As you can see, they're contrasting XT-286 and AT, further supporting that the XT-286 is not an AT machine. It might be AT class in the sense that it runs the same software as an AT machine, due to the same CPU, but it's an XT as far as the BIOS and expansion bus is concerned.