I don't know what Marriott's "official" policy is, but I can say that I have, on a number of occasions had basically the same thing happen to me. Personally, I haven't really worried about it and was quite happy as that allowed my friends to get into the room and start enjoying their stay.

I figured if the hotel ever let someone who I didn't know check-in, it would probably be corrected very quickly, easily, and without any problems coming back to me as the hotel didn't have any documentation from me stating someone other than myself was checking in. So there isn't really a downside to this (from my side at least.) The hotel may end up with some heartburn over it if there did turn out to be an issue, but not me.