Okay, so the two questions are:
(1) Is it possible?
Answer: Yes, you've seen someone else do it. I also accept that it's technically possible.
(2) Is it permissible?
Answer: No, it violates Youtube's TOS (see my earlier post). The TOS very clearly states that the only permissible use of Youtube content is through their player, and that you are not permitted to alter their player. Therefore removing the Youtube player so you can add your own skin is against the Youtube TOS.
Until I see a change in their TOS page I think that's the end of this discussion for me. Cheers