Clearly it's money and stadium - PawSox don't own McCoy - they'd own the new place, I think it's probably that simple.
Well, the Sox (aside from Lucchino) do not own the team, they do have an agreement with them to provide players. I am sure those agreements include some standard share of stuff. If the Sox had a big issue, they could easily switch to another franchise when the affiliation agreement ends.
That said, I think this move is just the new owners wanting to make the franchise more valuable by owning the stadium and all related revenue.