In many cases, quote questions can be answered by finding sources or direct evidence for the quote in question, and that ends the matter.
But some of the time, it all comes down to one source claiming that it was said... which could be seen as the necessary evidence, but it could also be called the original source of the claim, and be subject to the exact same question of "is this claim credible?"
As a result, it would generally be preferable to have multiple corroborating sources, or more direct evidence, in order to be able to definitively say that the claim is true.
What should be done when such corroborating evidence is not available? If a single journalist claims that person X said Y, and all other instances of the claim flow from that one, do we accept the journalist's claim?
Where there is no other reason to doubt it, I can't see a problem with accepting the claim. But what happens when there are plausible arguments for why the claim may be false on the basis of that source?
Usually, these arguments are much less solid than the typical standard by which answers are judged. But at the same time, it would be poor form, as skeptics, to accept the claim on a single original assertion.
This dilemma is exacerbated by the fact that much of the "reasons for doubt" would likely fall under "original research", at least to some degree or from a certain perspective.
One could argue that we would need a reputable source discussing these reasons for doubt. But if it were, say, a scientific paper that wasn't peer-reviewed, it wouldn't be unusual to identify reasons to doubt it as an answer where definitive confirmation or rejection isn't possible.
How should we handle this?