It was Snyder who tried to move the team in the first instance, not Brown (to this day, I try not to spend a dime in Snyder's Hyatt on Main St.), and I believe it was to Florida, not San Diego, to which he first tried to move the team. Interestingly, the Braves played a series of games in Toronto to try to broaden the fan base before moving.
Brown then got control and actually ADDED talent (Malone) before giving up.
And of course, in effect, he didn't move the existing Braves team to San Diego (and then LA); he moved the Celtics. He swapped the entire Braves team for the entire Celts team before the move.
I do not think, though, that this is what Wilson is up to. He may not care if the team stays (personally, I think he would prefer that it does stay), but he definitely doesn't care if it goes--he's not doing anything to try to help a move.