Sony may have done that but they would basically have no right to show that (in order to try to show what EA "lost") assuming Respawn did in fact go to them twice and Microsoft had to step in to save the game (or it wouldn't have been made at all). A game is better than no game, after all.
I think it's reasonable for Microsoft to want full exclusivity if they stepped in to save the game with their own money though.
Also, to note: Microsoft obviously didn't save the game out of the kindness of their hearts - they believed in Respawn's ability to produce a game that would ultimately have great results and be a game that could define their system. They were essentially willing to take the risk at the time whereas Sony was not so willing.
Well at least in 2012, they seemed to only want a year of exclusivity for their money (or the amount of money given at the time was only enough for one year of exclusivity). MS gets 100% credit for saving the game for this, because if EA really was going to dispose of this game and not fund it, then but for MS's involvement, this game would not exist.
I would assume that this initial influx of cash was enough to finish the game, or else they wouldn't be talking about one year exclusivity periods already.
In 2014 or whenever MS locked it up for eternity, that would be moneyhatting (note that at this time the game was essentially completed) because the game had gotten the funding to get made and MS had gotten the benefit for its money (1 year exclusivity), but wanted more. At this time, either MS saw TF as a bigger hit than it originally predicted, or given the Xbone's failure to outsell PS4, they decided to give something else for permanent exclusivity.
Which is why I said before, they saved it first, then moneyhatted it. In this case though, the moneyhat is not as bad as other moneyhats as they were responsible for getting the game made in the first place, but it's a moneyhat nevertheless.