False. This is basically Bruger King telling McDonald's that they can sell Whoppers and McDonald's then turning around a giving them away for free. Burger King looses a gang of cash.
I may be wrong but to me I think this is how it worked out.
MLB went to Sony during renegotiations and flat out said "we need this game on both platforms or we will not be renewing".
Sony said "we have little choice and it will bring us some more money selling on XBOX so ok".
Sony agrees and then PAYS MLB for the exclusive license and is most likely thinking "MLB 2022 will be our best selling year ever".
MLB and Microsoft desides that they should just go ahead and put the game on Gamepass so the game can reach the the most people the fastest and CHEAPEST way it can.
Microsoft is happy because they have an exclusive SONY title that they had to pay NOTHING for and all of their sports playing consumers are happy.
MLB is happy because they got a bag from Sony for the exclusive right, most likely a bag from Microsoft for making this happen and whole new side of gamers playing their game again.
Sony on the other hand got raped in the deal because they listened to MLB and did everything they needed to do just to have their product being given away for free on their rivals system while they're charging their customers full price for the game.
Thus is some of the worst business practice i have ever seen in my life. With this game being given away for the free it just destroyed any hopes of every seeing an exclusive title on cross platform ever again and could very well be the beginning of the end for MLB Baseball because if Sony didn't receive a bag (which I'm sure they didn't) what happens when it's time to renegotiate?
Sony is not about to renew their license if they have to give Microsoft the game and they are allowed to just give it away for free. At that point all baseball fans are stuck with R.B.I.
This is truly some foul business management.
Like @goatmane said below your post this is a multi year deal, and has been in the works for a while. Sony isn't getting an exclusive licence from the MLB. MLB has been about brand expansion for a while now and having their product on one system goes against their corporate goals
There's nothing Sony could do about this, tbh.