It's not a matter of "non-apple" bt keyboards. I have a freedom mini-duo keyboard that I can pair and use just fine (in HID mode) on my
iMac. I'm pretty sure my iGo will work with it too.

(interestingly, the freedom mini-duo will NOT work with my NIT)

I'm pretty sure it's a known/documented aspect of the Bluetooth HID profile, it's just not an aspect that seems to be in the open source BT stacks.