By saying that you remind the interlocutor that being rude is in fact an option (indeed a widely used one) and you may simply be rude ... ah the subtleties of communication.
Can't speak for the others, but by merely saying "please don't think I'm being rude ..." you explicitly remind the other side that being rude is an option, and that what follows should not be taken literally. Indeed why would you say "don't think I'm being rude" except if you already anticipated that the other side will take it as being rude.