That's not true

The testimony of a mentally ill person CAN be used to obtain a warrant, but the mental illness, if known, usually has to be considered.

A person who is in remission, for example, will likely be considered very credible. Someone not in remission, but whose illness does not include delusions, lies, etc., is also likely to be believed by a warrant-issuing judge.

Sorry, but unless a reasonable police officer or judge would have reasonably questioned the veracity of the testimony and did not, your counter-punch will go nowhere.