LOL. Ahh I think thats funny. Anyways, here lies the secret:
Hold W and A or D (doesnt matter which, usually it depends on how much space you have to either side). While doing this, the chopper should begin to spin, now simply make some adjustments with your mouse and you should be set. The chopper should start to stand up on its tail a bit and from there you just level out.
WARNING: If you havent managed to flip it rightside up by the time the chopper is done warming up, switch seats again and start over. Otherwise....bad things happen.
Heli physics really ruins alot of it for me. I know that its not the PR boys' fault. Being able to flip a chopper thats on its side (by this time it would not function of obvious reasons) is complete bogus and should not be possible.