Nouns frequently modify other nouns in English, and that is the case with passenger seat. It describes a seat that is meant to be used by a passenger.
Passenger’s seat, on the other hand, is the normal way of saying ‘the seat of a passenger’. It means that the seat that in some way belongs to a passenger. In this particular case it is an unlikely thing for anyone to say in that context, which is no doubt why your friend was corrected. It would, however, occur in a sentence like this:
"I'm sorry, sir, I'm afraid I'm going to have to ask you to move. This is another passenger's seat."
4Interestingly enough, because of the way seat begins with an "s", had you heard your friend - instead of reading what he had written - it might have been difficult to tell whether he had said passenger seat or passenger's seat. Conceivably, someone could say this the "wrong" way for a long time before being found out. – J.R. – 2013-02-01T18:42:28.453