I maintain Hamilton's "best shot" had nothing to do with Balsillie and was way back in the early 90s. And that group got picky about how to pay the expansion fee. Pennywise, pound foolish. (FWIW, the requested fee then was $50mil which inflated to 2023 is $112 mil. A stone cold bargain compared to the money that could have been made.....).
Of Balsillie's attempts, the one that truly "got away" if he'd played the "right" way was the one he never (publicly but I always deeply suspected he did so privately) bid for: the Thrashers. Because that was the one team where the owners really didn't just threaten to throw the keys on the table, but honest-to-goodness threw the damn keys on the table with the city doing nothing other than saying "well, there are those keys sitting on the table alright."
While Balsillie was busy blitzkrieging everything is sight, Chipman & co. were quietly making nice and got Winnipeg a team at a tidy bargain.