Sometimes the citation IS already given, but not in that exact spot. Where an entire paragraph or group of paragraphs is taken from a standard source in the subject it should not be necessary to reference every detail of that passage, and it should be sufficient to state that a citation applies to the entire range.
That is exactly the situation where it would be appropriate to just remove the {{fact}} tag. (With an appropriate explanation in the edit summary)
Negative statements are trickier because hard evidence that something did _not_ happen usually cannot exist. The implicit message when we say that something did not happen is that we have no evidence that it did. Perhaps that requires a convention about negative statements. Attributing a claim that something did not happen, or showing why it was impossible for it to happen would remain a stronger statement.
Pretty much the only acceptable method is finding a reliable source that said it didn't happen. Proving that it is impossible for it to have happened sounds like OR to me.