Earlier quoted context omitted.
Doesn’t mean you have to accept it, it just means that there’s very little you can assert as false. Snopes does that every day with very little to prove it other than the desires of its readers to agree with them.
"False" is clearly shorthand for "there is no evidence that this is true." If I wrote "brightball beats his wife" and then said you couldn't really say it was false because you couldn't prove it had never happened definitively it would be outrageous, right? Nobody would accept that as a reasonable argument.
This is why gossip and rumors are such a powerful thing. We all want to think that what we know or what we heard is true, but very few people are willing to accept that what they heard might not be accurate. Especially once they have repeated it to someone else.