you are correct. most receivers don't have a 3rd prong, because it's not really needed. however, it's not safe to say that the receiver isn't grounded because it's lacking a prong.
the 2nd and 3rd prong are the ground and the neutral of the circuit. they physically tie together back at the main service panel of his apt complex. typically, only motors and surge protectors have the 3rd prong, so a fault current on the neutral can be detected, which would cause the breaker to trip (so long as it's a GFCI breaker or outlet).
you'll often see 3rd prongs on equipment that has a heavy current draw (like microwaves), or equipment that runs a chance of accidental unbalanced motor loads (like your vaccuum cleaner).
so long as his apt complex has their installation per code (God willing
) he should be in good hands.
you brought out a very good topic!