Well the headlines have been very misleading because I have seen things like "Red Sox purchase minority ownership of Pawsox" in many places. Even on TV, lol.
In any case, I don't see anyone spending the kind of money it will take in land, infrastructure, and construction costs just to be able to say that they own the stadium.
Not with the ROI that the Pawsox provide.
But you never know. Stupid decisions are made a lot.