The implication is then that if you can't advance your career in this organisation, you will do it in another organisation. The VP will then be stuck with the flakey supervisor, no succession plan for your role or the supervisor, no documentation around how you do your job, and no opportunity to call you if there is a problem (all of which the VP would have if you got an internal transfer or promotion). The VP may also get an employee who just does the job, without the covering for the flakey supervisor that you no doubt do.

The evil part of me suggests that if the VP reacts negatively to your request, let it go for a week or so, then ask the VP if they will act as a referee on your CV. But I wouldn't be that brave either. However, I would ask the other supervisor to be a referee – even though you haven't worked with him, he obviously has a high opinion of you. If word gets out that you're after a new job in another organisation, they might be happier about giving you the transfer you should have got before.