Seems very susceptible to cheating...as in player X, who sucks, can record superb (but fake) stats on this app. Correct? Or is there something to block this?

I would say ~90% of the stat recorders for our iOS app are coaches who use the tools to scout players or help review strengths and weaknesses of their players, so we are not as worried about incorrect stats. Anybody can record stats for any player, but the owner of the player profile must approve the stat line before it becomes public, so that prevents others from purposefully harming another players stats. Ultimately, the correctness of the stat line falls upon the player (or owner of the player profile), so they put their integrity on the line when updating or accepting their stat lines.