If you use regular steel wool on stainless steel you will get rust no matter the atmospheric conditions or rating. The abrasive you use (iron wool) will transfer to the stainless and cause rust.
Go into any welding shop and see how they segegate their tools according to steel or stainless. From torches to polishing everything is clearly seperated between steel and stainless steel.
To clean up the rust, use a navel jelly first to dissolve the iron oxide deposits, that will get most of the surface discolation off. Next use a stainless steel polishing device. If you use metal, make sure the rating is equal or higher than than the base metal. 3M makes nonmetallic polishing pads in varying grits that will achieve the desired finish. grainger.com or mcmaster.com
Follow the polishing with a good coat of wax. Stainless means just that, less stains, but it will stain