> Let's say the head of an agency decides their interpretation of the law is X, but the President thinks it's Y. You can't bring them to court because X and Y fall within the interpretation of law.

Uh, who is “you” in this scenario? Because for most reasonable values, yes, you can.

Differing interpretations of the law by different executive branch officers have never stopped outside parties from suing those executive officers over their execution of the law, with the courts ultimately deciding the correct interpretation (sometimes with some degree of deference, but never absolute, to executive interpretations.)