IBM 5161 - 5160 Incompatibility
The 'IBM PC Family Service Information' document includes the following in the 5161 section:
"Note: This unit is not supported on 5160 Models 088, 089, 267, 268, 277, and 278."
Those were the later 5160 models, the ones released in 1986.
There is no detail on IBM's meaning of "not supported".
I suspect that this may be BIOS related, based on what I see in the power-on self test (POST) within the BIOS.
If you look at the POST breakdowns at here, the 01/10/86 BIOS (the first of the 1986 dated BIOS releases) is missing a 5161 related step:
I do not have a 5161 to test the BIOS hypothesis.