If we're going to assume that what they say is noteworthy anyway (may not always be the case, see the discussion Oddthinking linked), then I would say that otherwise the determining factor is how visible the claim is, because that is a good proxy for whether it is widely believed. Right off the bat, a Trump speech might start with around 47 million US viewers, and over time the viewership grows as people around the world watch. I assume your grandfather does not have such an audience.
Similarly, if J.K. Rowling posts something on Twitter, she will have a wide audience.
If the claim you are intending to evaluate has an audience of less than 1000 people, then I think it is safe to say it is not notable. Why 1000? The smallest country (aside from the Vatican City) has a population just over 1000. I think a claim that might be believed by a whole country (even if that country is Tokelau, a dependency of New Zealand) is worthy of consideration, thus notable.