Whenever I have rust-looking spots like that, I take a small piece of aluminum foil and rub... it does come off. I'm guessing a very fine grade of steel wool would do the trick too. But whatever you use, test it gently first, to make sure it's not causing deep scratches.
If it can't be fixed with chocolate... why bother?
Just to second, SS can rust, depending on the grade and other metals in it. I have some SS dog dishes and buckets that didn't show any signs of rust spotting until I started putting them in a dishwasher. Now I have a few starting to spot up on me, but I can get the spots out with a scotch-brite.
And I "third" it. The metal composition of products labeled "STAINLESS" vary by manufacturer. Some compositions will rust. Many brands of automatic dishwasher detergent include an oxygen bleach which accelerates the oxidation (rusting) process.