I have to admit that I don't know the composition of Reynolds tubing but in general, SS tubes are resistant to rust but aren't rust free. If you live where sweat will drip onto the tubes and you don't clean it off, even stainless will rust. Different tubes, depending on composition will be more or less resistant.
KVA is another player in the stainless market. Their tubes definitely come in at a lighter weight than standard chromoly and are nicely finished.