Before you start your first game, the fours server will create an token with your data (user changeable username, stats and an id). This token will not be persisted by the fours server. Instead your device will save the token. While playing against other players (not bots), participants of the game can access the the data (username, stats and id) stored in the token, because the fours server will store this data while the game is running. Since you can choose the username, the data is not linked to your identity.
By playing fours, you agree not to cheat in any way. However, if the developers are persuaded that you have been cheating, the developers are allowed to ban your account.