Is the statement "Claims demand evidence" always true?

[Mudhammam]

Precisely, which is why your assertion that those asking for evidence of claims of existence are mistaken is, well, mistaken.

Well, that's granting that a claim can only be justified by evidence. But that itself is a claim that I don't think meets its own criteria, which is the point of this whole thread.  Unless I am misunderstanding what you mean by justification or evidence.