It's an interesting legal question. The names and stats are clearly in the public domain. Even what teams they play for. What's not is their likeness, their jerseys, or to otherwise make the game look like the players are sponsoring or promoting the game. How the stats are displayed is a copyrightable thing, as well. It's obvious that fantasy sports, where you pay to join a league and they give out prizes, is gambling by the legal definition. The NFL has been making money off the fans who play these games, and they lobbied the govt. to make the games legal. If they're cut out of their revenues from the activity, they're not likely to keep it as something legal.
This is a perfect example of cutting off your nose to spite your face....Fantasy Football is part of the reason the game is so popular and part of the reason the players make so much money....mess with fantasy football and the popularity begins to falter some and the TV contract will eventually show that....