I think it worked the other way around too.
For example, I think that for a certain amount time Meyer Lansky was thought to be a Mafia or Cosa Nostra member of high rank
Not sure if that's what Law Enforecement thought ,but that's what I think a lot of people believed,based on things they'd read or maybe say on TV or movies.
100%! There are many examples of that. And as you mentioned, Meyer Lansky is a perfect one.
For many years he was considered an actual "inducted" member of the Mafia, when the reality was a bit different.