Burgess was thinking of retiring following Doohan's retirement, reports said he no longer wanted to be involved as seeing rider after rider get seriously injured was getting to him. Rossi was wanted by Honda on the 500 but Rossi would only go there if Burgess was his crew chief. I imagine Honda wanted Rossi enough that they offered JB a salary he couldn't refuse so he stayed. Not really Rossi talking him out of it and not sure that retirement has been mentioned since.
It's interesting this time that Rossi must have been keen enough to vacate Ducati and get back to Yamaha, as he just went without any demands that his crew going with him were a pre-condition to him signing. Now he has to hope that Yamaha agree to taking them back as well. I'm not so sure they will as they would surely know he would want them, why not contract them all at the same time? Seems strange.
Surely Yamaha aren't playing games and forcing a bit more humble pie with a covert statement of you walked out, so you come back on our terms. This time we're in charge, not you?
The other things to consider with Burgess are that he can't be far off retirement age now, doesn't need the money, his wife has been seriously ill and he has actually been a bit disgruntled with Rossi's attitude towards the Ducati - it's been obvious in some of the interviews he's given. Not a falling out but definitely a 'FFS just ride the thing' exasperation.
The rest of the crew I've no idea about but the bottom line with Burgess after all else above is considered, is - has he just had enough of it by now and does he need another 2 years. He may feel he has nothing to prove, so why would he need it?