It tells us that people are willing to sign a petition to ban a thing while clearly not having done their research on the thing, just because an authoritative-seeming stranger told them something plausible. It means that such petitions shouldn't be taken seriously; and, to the extent that they are serious, it implies something about people's recklessness with regard to policymaking.

(I wonder how such a survey would fare today, when most people have smartphones with browsers and an internet connection.)