I think you misunderstand me: I mean that you can only use this argument against a well established, probably experimentally well supported theory, if you have

I think you misunderstand me: I mean that you can only use this argument against a well established, probably experimentally well supported theory, if you have at least some experimental results that are contradicted by the theory (and preferably explained by your alternative). There are many crackpots that 'have been shocked to realize that library books and teachers were wrong and that they should trust their own thinking in the face of concerted opposition'. Only slightly different from the original, but the italicized words make a world of difference. Einstein's (special) theory of relativity faces scores of opponents that 'trust their own thinking', despite not having a single fact that casts doubt on it.