Ger,
The active ingredient that makes this stuff work is some kind of acid. I dropped some of it on my aluminum XDeck and it ate the finish right off of it.
I rubbed it on my car trailer and it had the same effect. Now I know aluminum is not stainless steel, but they use this stuff diluted 30:1 to clean mildew off of paint. I was using it straight out of the bottle.
It may not hurt the paint and it may not hurt the stainless, but until I have a little more experience with it, 10 minutes and a $2 drop cloth vs my experience with the cost of paint is an easy trade-off.