In the USA, I do not think this is true. Like any words or phrases, either one of these could be rude if used sarcastically or dismissively. But I think that "sure" is more likely to be interpreted as rude in a more formal setting - and neither one is likely to be rude in an informal conversation with a friend, unless it is intended to be rude with the tone. For example, if a lawyer is in court, and the judge asks him "Do you intend to file a response to this motion?", the lawyer might respond "Of course" (more likely "Of course, your Honor.") without the judge thinking him to be rude. But if he replied "Sure," the judge will probably be mildly annoyed, if not offended. "Sure" is more informal and not appropriate to the setting. However, I think this is a quirk of American usage. The phrase "of course" is somewhat inherently rude because it is dismissive of the concern behind the question being asked. "Of course" essentially means "Yes, obviously" and could be interpreted to imply that the asker should have already known the answer to her question. In the USA, "of course" is so frequently used casually and innocently, that most of this implication has fallen away.

It depends on what situation, but in the right situation either one of them is rude.