Steel wool fibers don't imbed in stainless. Just clean the residue off after using it.
Correct only to the extent the steel wool does not embed.
The steel wool leaves carbon steel smeared on the surface of the stainless steel, especially brushed stainless steel (all those tiny brush marks are scratches in the stainless).
If not protected from the air with oil, the carbon steel on the surface can start to rust, leaving rust on the stainless.
It is called stain-less, not stain-none.
There are more corrosion resistant alloys than the ones used in firearms, but they are vulnerable to other chemicals.
Most stainless alloys are vulnerable to chloride ions, as in the ones in your sweat form Sodium Chloride (ordinary salt).
The chloride ion can react with the chromium layer that protects the steel.
Once the chromium is damaged the iron in the alloy is exposed.
Passivating of stainless steel cleans off material that may be left from machining, or exposed in the alloy when the metal was machined.
After a thorough cleaning of any shop debris, an acid bath is used to remove any iron that may be on the surface (from cutting tools or the alloy).
This allows the corrosion resistant passivation layer to form uniformly on the stainless surface.
Damage the passivation layer and corrosion can still occur.
An oil film can help prevent damaged passivation areas from corroding.
This is the same reason you should not use a steel wool pad to scrub you stainless kitchen sink, or even a granite counter.
