Simply remember that the aim of the game is to take your opponent's King. (Of course, the game actually ends when it's impossible for one player to prevent his King being taken. i.e. when he's in checkmate).
If you take your opponent's Queen, his Rook (=Castle) can immediately take your King. The fact that you might be able to take his King afterwards (i.e. he'd be in check) is completely irrelevant, since the game will have already ended.
So your friend is correct.
Chris
(Regional Coach, British Chess Federation)