Stainless steel is rust-resistant not rust-proof, especially if the bike sees the outdoors a lot, it isn't uncommon for screws to get a fine sprinkling of brown spots. The good thing about screws is that they can be easily replaced.
If you were very enterprising you can probably replace all your screws with titanium ones, they are slightly stronger than steel and are less temperature dependent (not that any of this really matters on a bicycle) and are fairly resistant to corrosion AFAIR a little more so than stainless steel.
Painted components (like your bike frame) are naturally rust resistant because the paint prevents contact with oxygen, which means that the metal can't oxidise and also explains why its not a bad idea to touch up on large paint chips or scratches with touch up laquer.
ADDED a quick wikipedia glance explains that while stainless steel gets covered in rust, unlike regular steel the rust is passive meaning that it will just stay there (looking unsightly). With regular steel, rust has the nasty habit of eating away at the metal (it is an active oxidation site). The rust on stainless steel behaves like a coating that prevents further oxidation.