As I was about to mention yesterday, "Stainless" means Stain Less.
It does have a lot of iron in it and under certain conditions it will stain or even rust.
Cleaning a Stainless barrel should be done after shooting just as though it were a carbon steel barrel.
By the way. Those ads that say you don't have to clean a stainless barrel were written by the Advertising department, not the engineers that know about these things.
Not that Ad guys would tell untruths to sell a product but if they said a 3 legged dog was the "New, High Efficiency Model", it wouldn't surprise me.