Except for Thomas, who wasn't even a high priced FA. I don't understand why teams splurge on goaltending when they should be scouting.
There is a simple explanation that could explain this correlation. It involves 2 claims:
1) Elite goaltenders are more likely to win big games
2) Teams are unlikely to trade elite goaltenders
These two claims together would explain the interesting statistic you point out.
The first claim is almost certainly true. The second claim seems to be true as well, as the only elite goaltender in the last decade I remember being traded is Luongo from Florida. So teams essentially never trade an elite goaltender.
It counts in the sense that all the winning goalies since 2006, Thomas included, came into their own on the team they won with. None of them were high priced free agents.
All of them were on stacked teams and were good enough to win when it mattered.
It's just more evidence that throwing big money and years at a UFA goalie is a terrible idea. See Bryzgalov, Huet, Khabibulin, Luongo... I can't think of any big money goalie that's ever lived up to the contract.