The thing is that "No Evidence" is just flat untrue. If Crazy Carl says that aliens abducted his prize turnip, that is in itself evidence that aliens did the deed. It is wildly unpersuasive evidence, but nonetheless evidence. People like to believe that "someone says" isn't evidence, which is wildly disconnected from how human society works. Even alleged facts boil down to "someone says". The vast majority of people who know the constant of gravity never measured it for example, they just work with what someone told them - an authority figure saying something is quite strong evidence.

Having evidence for untrue things also turns up naturally because of statistical mirages.

"No evidence" is a phrase that gets used in untruthful ways. There usually is evidence, of everything. True, false or irrelevant - there will be evidence of it in some form or another. The question is what standard the evidence reaches, not whether it exists.