Yeah but not really. I seriously doubt Joe was the one who decided to fire Dillon (or Castro though that was a much easier call). He also didn't get to hire any of this staff in the first place (except for Dillon and Price merely because those positions had already been vacated).
So yeah, sure, the manager should always get to pick his staff but he didn't pick most of these guys, and it was just a coincidence that Thomson was already here. If you really want to make a statement about his autonomy and power you'd also pick up his option. Charlie didn't get to pick any of his coaches when Gillick decided to keep him and I actually think it would be good if Fuld and Dombrowski tried to put some new voices into the mix.
A combination of the same old staff that has failed for four straight years under two different GMs and managers combined with the staff that got Girardi fired in New York doesn't excite me. (Or rather, Long is one of the guys Girardi cut loose in New York before his own time came to an end later.)