Let's go back to first principles.
We want claims to be notable so we know the large effort of producing a quality answer (and editing the question into shape) is worthwhile - that it affects a belief that lots of people share, rather than some spurious conjecture that a couple of people drinking in a pub came up with.
We can't easily know how many people believe some claim, so we use a much cheaper proxy: find a source that makes the claim that is widely read or listened too - such as a newspaper, celebrity utterance or viral post.
However, if there is a reasonably trustworthy survey that shows that a significant proportion of the population believe that humans never walked on the moon, that is actually better evidence that it is widely believed than some celebrity saying it.
So, as the survey is used on the cited question, I am happy that it is notable.
[I have some other concerns about about the clarity of the question that I am in a chat with the author about. They may or may not be resolved by the time you read this.]
What does "reasonably trustworthy" mean? I'm happy to leave this vague. The definition is about convincing people to spend effort, and that is going to always be a fuzzy line.
There is a different way surveys might be cited - where you doubt the conclusions of the survey, not the topic the survey was about.
For example, I recently read that 15.9% of Australian households have a pet bird.
That does not match my anecdotal experience in Australian households and I am personally incredulous the figure is so high.
It would be reasonable to ask if the survey result is accurate. There may be criticism of the survey process in the literature or there may be competing surveys that give conflicting results that could be used in an answer.
[I haven't asked such a question because the source is the Australian Bureau of Statistics, because I cannot imagine another source that would be more trustworthy on this topic.]
