Your list has a problem. It’s a false dichotomy. A class can have a method of proving while also being a fake claim so long as there is either: a potential reason for not using the ability or: a method of faking it anyways.
Something who only has something like that is what I would call semi-fakable:
Princess, Hunter, Observer, Court Wizard
Of those observer is perceived as being catagory 3 (unfakeable)