I booked a room a month ago for my parents using my points. I put my father's name on the reservation, but given that our names are the same (except for the suffix) the hotel treated them as if they were me. So it does seem to happen.

My suggestion though is to not expect it to happen and if it does, great. Your parents may get a little better treatment. If it is OK for them to stay in the room category you book and not get Plat benefits, then fine play the game and maybe everyone is pleasantly surprised. But if you really want them to have that room upgrade or something else, I would suggest calling the hotel directly and to try and work a deal with extra points or cash or something. That way there are no disappointments.