Nickel steel will rust, firearms-grade stainless steel just kind of gets blotchy and discolored, and will pit badly if you let it. It will eventually rust if you let it, but the discoloration you see is in fact oxidation, just like surface rust on carbon steel.
One advantage the older guns had over the newer guns is they absorbed a lot of good old-fashioned oil during their lifetimes, as silicone lubricants were not available until the 1950s or so. Silicone goes on thinner and just on the surface, so it will also wipe off or wash off easier, too.
Lots of opinions on this, but it all comes down to what is the cheapest and easiest steel to machine, and that is what they will use to make your next gun. If you remember back in the 70s when stainless first started making an appearance in mass produced guns, there was a lot of griping about how badly stainless galled. That is due to gunmakers choosing a grade of stainless that was easy to machine but was not well-suited to making parts that slid against each other under load. Some gunmakers actually folded because their guns were failing when fired. They looked fine, but you couldn't shoot them and expect them to make it through the day without problems.
On the other hand, it did spawn a lot of products specifically for lubing stainless, like RIG gun grease, Super Lube, RemOil, and others.