ha, I actually know about this.
One of my online businesses was going to use content from another website, but I wasn't sure if i was allowed to "take" the content. This wasn't articles or anything, just public information - not much different than stats or the weather history.
What I found out, was that you can take and use this type of stuff so long as you "creatively alter" the way it is used. And by that I mean you can't just copy and paste, you need to dress it up, make it look a different way etc.
There was a supreme court case once where someone used all of the exact content from another phone book to make their own phone book. The court ruled against them, but said if they hadn't just copied the first phone book exactly they would have been fine. If they had organized it differently or added some of their own content or design it would have been enough.
I'm not positive if baseball stats fall into the same category, but I would assume they would. Not sure how to alter the stats though....
MLB would catch hell in the court of public opinion if they did try something like that