publications - What do I do if my supervisor insists that the classical CLT is false and wants me to write that in my paper?

We are in a physics department. My supervisor, upon reading a Physical Review Letters (PRL) paper, concludes (and claims that the paper also concludes) that the classical central limit theorem (CLT) is false under the (usual) assumptions stated. He insists on this result and wants me to say/imply that in my manuscript because he finds fault with me making use of the classical CLT in a few statistical tests that I have utilized in the paper.

Question: (1) Would you say that my supervisor is scientifically incompetent? (2) How should I handle such a situation?

The paper is single-authored by me but he says that the university requires him to vet journal submissions (for quality) even though he is not a co-author which I accept.

(EDIT) More info regarding the context:

Just to clarify further, copied from my comment below: In my paper, I was simply stating the assumptions of classical CLT so that I could make use of the resulting normal distributions for some statistical tests. It was not a particular usage/application of classical CLT but simply a statement of the assumptions that would need to be held to recover normal distributions for the application of statistical tests I was using.

Answer

(1) Would you say that my supervisor is scientifically incompetent?

If he says the CLT as stated and proved in textbooks is false, he is obviously wrong. "Scientifically incompetent" sounds like a very sweeping statement that I would avoid endorsing given the information currently available. He could simply be misunderstanding something in the language of the paper, or his knowledge of rigorous math could have an embarrassing gap (wouldn't be the first time), or it could be a failure of communication between you where you have a subtle misunderstanding of his position.

In any case, textbook CLT is correct, no question about it.

(2) How should I handle such a situation?

An honest intellectual dialogue with him to clarify the issue would be ideal, if he is the kind of person who can have such a dialogue when he is in the wrong and not back himself into an emotional corner and become upset and unable to reason. If you think that's risky, try to find another professor you trust and can consult about the issue, and if they agree with you, ask them to participate in a discussion with the advisor to make him understand your point. And try approaching any discussions with an open mind, in case it's you who are in error about what his position is exactly.

Finally, it's possible that your advisor really is scientifically incompetent, so if you are unable to make him come around to your view and conclude that he is intellectually unsuited to be your advisor, you should probably switch advisors. In any case, under no circumstance should you concede to his demand to deny the truth of a standard formulation of CLT in your paper. Good luck!