This 100%. Plus it's not Sony's fault that 2K ended their MLB license back then. The Xbox fanbase had MLB games on their system, they just didn't buy them. The Show outsold and eclipsed 2K MLB games critically and commercially. This "rumor" wasn't even a rumor, it was just passed around on gaming threads by users who have no inside knowledge of it. It gets spun so many times on so many gaming sites that people just start believing it. Rather than that, those other console fans should just celebrate getting a AAA baseball game in the Show and appreciate it. On the matter of this logo, it will probably be on the Show boot up screen from now on even just as marketing for the Sony game on another system.
The inverse is the more plausible story. MLB was tired of making baseball games that no one would buy on systems where it was the only baseball game. So they turned to the leader in the space and gave them full rights, creative control and % of royalties in exchange for the game being multiplat. Starting in 2021, there will be no MLBAM produced R.B.I baseball game, MLB the Show will be the only game in town.