Evidentials appear in many languages of the world. Many languages have them as an integral part of the verb morphology, but a slightly more limited distribution is not entirely inconceivable. I have been thinking a bit about what particular types of words and constructions may be likely to attract evidential marking. I make no claim as to completeness.
Such and thus are interesting - they're partially adjectives/adverbs, partially demonstratives. Basically shorthand for "like that" or "like this". Some languages have the same levels of deixis for their correlate, such as Swedish "så(da)n där/så(da)n här" which perfectly maps onto den här/den här. "Så här", "så där" basically provides two forms of 'thus' with a deictic distinction.
So, with these, some types of statements may actually invite evidentiality.
Particularly conjunctions that introduce subclauses.
Certain adjectives and nouns relating to status in the eye of the law
criminal, murderer, etc, but also possibly statuses that aren't directly connected to culpability: heir-to-be, engaged, bastard