Or it could arise if a White knight captures, say, some rook on d7 and it would currently be Black to move.
Yes. My point was really that you specified White to move (and even in the absence of a specification I think White to play would be conventionally assumed).
You get a stalemate when your opponent cannot move, but they are not in check.
So if my opponent (not the pieces) is paralysed and his/her paralysis has not been checked by a doctor, does it mean the situation is a stalemate?