Stainless Steel is still primarily iron, that will rust, except stainless steel contains Chromium and Nickle that creates a Chromium Oxide layer on the surface when exposed to oxygen to prevent rust. That is what is Passivation.
I don't know if machining from Carbon Steel tools, if not passivated, can cause surface rust, I have no reason to doubt that assertion, but depending on the alloy, conditions and circumstances, sooner or later rust will appear on stainless steel. Clearly, cutting away the old oxidized surface to create a fresh one, would remove the original passivation. I don't know if the contact with the carbon steel during the machining might do something to leave carbon behind, or stave off the natural process of passivation.
I've seen stainless steel rust, heck, the O.P. is photos of rust on stainless steel. Usually its exposed to heat, salt or chlorine that I've seen rather rapid rust, but still far slower rust than carbon steel under the same condition. So I don't if stainless steel always rust, just much slower than other steels, or if its a matter of it only rusts if the passivation is prevented by the conditions.
