I think he’s just taken the first chance that’s been presented to him. Would one of those clubs have approached him? Possibly but then again they may well have overlooked him. I’m guessing that he wasn’t too confident of job offers from better clubs than Sunderland or else he would probably have bided his time.
The other side is that if he does manage to turn Sunderland’s fortunes around, his reputation will be greatly improved and there’s a good chance that a bigger club will come in for him once he’s proved he can do a job at club level.