"They had contacted us warning that we were using copyrighted data" last I understood you can't copyright data or facts [in the US]. You can own copyright to a particular published format though. One can't copy and publish a phone book verbatim but you can certainly scrap a phone book for its data/facts and publish them in a different format.
Now I'm not sure if this is a slam dunk. My friend works developing a fantasy sports startup, he's talked about all kind of legal grey areas around the legality of where you get those stats. He didn't go into specifics though.
