What they could do, and what they might try to do, are two different things. Sports journalism talks about teams and players with impunity, as it’s considered to be news reporting. But the team names are considered trademarks of the clubs, and the clubs have assigned the administration of those rights to MLB, so MLB’s lawyers might take the position that use of those trademarks by another party in creating an entertainment product requires permission. Sort of like retailers who have to resort to circumlocutions like “be ready to watch the Big Sunday Game on your new 1000-inch hyperplasma TV” instead of saying “get yerself a new TV in time for the SuperBowl”. If there’s one thing the last 15 years have made clear, it’s that there’s no position so ridiculous or asinine that MLB’s management and lawyers won’t try to take it if they think it serves their purposes.
Like others, I can’t imagine what end they think they’re serving by discouraging disclosure of how to cork a bat (it’s information that’s potentially useful to fewer than about 10,000 people, since only the majors, minors, and a few summer amateur leagues use wooden bats), but I’m sure it has something to do with the “image” or “integrity” of baseball as perceived by Bob DuPuy and his minions.