The key is "assuming I would not be able to find another job that would pay me at my current rate". I don't believe Fitz is thinking that he cannot be a starter in this league besides in Buffalo. I am sure he believes he could start (besides Buffalo) for Arizona, Cleveland, Jacksonville, Oakland etc. And even if he were to take a substantial pay cut to be a backup, may be he wants to be a backup on a super-bowl bound team like Atlanta or Denver or may be he wants to be a backup on a team like Philadelphia whose starting QB is injury prone and likely to miss games.
Finally, if you were not just asked to take a pay cut, but also asked to demote yourself in your role in the company, I highly doubt people will stay in that job forever.