Is the statement "Claims demand evidence" always true?

[Mudhammam]

 "Claims demand evidence" would apply exclusively to the first group, while "claims demand reasons" (that is, right or good reasons) would seem to apply to *all* claims.  

I might modify this to avoid an infinite regress of reasons by making a similar pragmatic appeal as rob mentioned, namely, an appeal to the utility of right reasons in actual experience; but then it seems that, on the one hand, evidence, to even get off the ground, requires reasons that are accepted as true by definition; and reasons, on the other hand, which we justify as true by definition, are only worth as much as our experience shows them to be rationally required.  It is as if reasons and evidences must support each other for either to do work, though the former still have greater reach in that they can take us to new heights and depths of knowledge of which evidence has yet to corroborate; but I don't think the same is true vice versa.  Evidence presumes some rational context from which to derive a meaningful interpretation.

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Not so. If this were the case, then there would be no distinction between what can be imagined and what is. The idea of 'justified true belief' can't be so easily dismissed.

The distinction between what we can imagine and what we are justified in believing as true would remain; as well, so would the distinction between what we are justified in believing as true and what is actually true.  I believe that we can be justified in a belief given our current reasons or evidence, and still be ultimately wrong about that belief.