I didn't say "must" - I said it CAN. I take issue with the statement made above that "you can't make stainless rust by sharpening (a stainless steel blade) on a rusty stone." That is false. It can happen.
Whether it would actually happen depends on how thoroughly you clean the blade. Using a stone by hand would be less likely to cause problems than using a powered belt as well. Either way it's not a massive issue. Any particles left on the blade would be a sort of catalyst point for rust to start, so a few particles might result in a few little rust spots. It's not going to instantly rust the entire blade. Aside from that, unless the blade is left to sit and not used, the mere wear from use would probably be enough to keep it from rusting.