Well, the simple answer is that apps are tied to an account. If the OP doesn't mind being logged in as him on his parents iTunes (and bear in mind that the password will also need to be stored as every update will need it) and being treated as one of his 5 allowed devices it shouldn't be a problem.
If he wants to keep things separate however, then what I said
Appleblinkers again? No - it's like saying you can never sell your boxed copy of Photoshop, not even when handed over, keys and all, with the PC. It's a problem now that others are adopting it as a successful model - I know I'll probably never see it on an Apple product (because of course the total lock-in is part of the strategy), but while it can't be a free-for-all like Maemo, I'd definitely like a 'reassign account' or 'I've sold my phone to x' option for other mobile OS's.