I don't think that people believe that everyone claiming to be poor is actually rich. They might, however, believe that many people (not everyone) claiming to be poor are secretly richer than they appear (which is probably not "rich" most of the time).

I am skeptical about attempts to analyze why one's political opponents believe things, because it's easy to strawman in this manner and generally use it as an excuse to treat one's opponents' claims as not worth addressing.