Yes, stainless steel corrodes. A dangerous type of corrosion that often is invisible as it occurs beneath the surface or in tiny pits that are hard to see.
It is not possible for the mechanic to visually inspect a stainless steel part for corrosion pitting and make an airworthiness assessment. More advanced NDT is required to expose the pits, survey their size and depth, and make a proper engineering decision. Nevertheless, this should not prevent the mechanic from doing a visual inspection as often it is the only means available. Regulatory authorities (and others) should realize that a positive outcome from a visual mechanic inspection does not mean that the part will function as the engineer intended.
Pitting corrosion attacks in a very localized manner. This highly focused corrosion creates pits or cavities in the surface of the part. Very often the part can be deeply penetrated by corrosion pits while its surface remains close to free from any corrosion. Corrosion products can hide such pits in an apparently devious way, making them appear to be much less severe than they actually are. Pits can be narrow at the surface and not look like much but be very deep or have subsurface cavities. Subsurface cavities can come together. Just like termites, most of the action is hidden beneath the surface.
The problem of stainless steel failure caused by corrosion is best exampled by the failure of stainless steel turnbuckles on a wide range of aircraft. The NTSB issued NTSB Safety Recommendations A-01-6 through A-01-8 to inspect aircraft turnbuckles, MS21260-S4 and AN669. Nevertheless, various government agencies recommend only a visual inspection as the sole means of preventing loss of aircraft control.