I don't think it's really a big coincidence. It happens all the time in baseball, and there's no cap: player delays surgery to try rehab, rehab fails, player ends up getting surgery months later and missing more time than they would have if they had opted for the surgery immediately.
I think the timing lining up in a way that's favorable to TB is a lot more likely than a) a team actually approaching a top-10 player in the world and asking him to needlessly sit out an entire season in the middle of his prime, and the player actually agreeing to do it. I don't think you become as good as Kucherov if you're cool sitting on your couch in your age-27 season instead of being out there contending for scoring titles and MVP awards.