No they did not all rust out.
The Corvair was GM's first unibody (unitized body structure) car. The modern equivalent of what we would call monocoque today.
Consequently, early unibody cars had lots of spot welds in the structure itself. Spot welding technology of the era stressed the metal and made the two joined panels stressed and "weld thinned" the metal in those areas. Weld thinning is what happens to metal when you heat it up and cool it down quickly.
Also primers and paints of the era were solvent based and did not adhere well to the welded areas causing some rest to set in. Add to that, that owners who didn't rinse the road salt off and well.....you know the rest of the story.
Spot welding is still used today by almost every car manufacturer, but primers, sealers, paints, and metallurgy is so much better. I suspect in the near future we will see car bodies glued together instead of spot welded with catalytic adhesives where the bond becomes stronger than the metal itself. These adhesives are already being used in the air frame industry and chances are that you have flown on a commuter jet that has had the fuselage skins bonded on by these types of adhesives. If memory serves me correctly, I think Ford is now using adhesive attached panels on the new aluminum skinned F150.....don't quote me on that, but maybe someone on BITOG can verify that.
Another thing to note about body assembly and manufacturing technology of that era as compared to today. Cars then were engineered to be consumed and manufactured at the lowest possible cost. They were also meant to be repaired in the event of a reasonable collision. Do you think that GM, or any other mfgr. of that time period ever thought of designing their cars to last well into the 21st century. They only wanted them to last long enough for you to see the requisite value, so that you would then trade it in on new model to "rinse and repeat" the process over and over again every few years.
Today cars are engineered to be assembled and not repaired.....referencing the body or coachwork of the car. Cost is still a consideration, but not repair. You may yourself, or know someone else who has experienced having a modern car "totalled" by the insurance company after what seemingly does not look like a large collision repair. Why? Labor is now expensive and materials are cheap by comparison, opposite of what was true back in the 60's and 70's. Plus the insurance company doesn't want to deal with the liability of a "come back" from a repaired car, or risk the insured to compromised structures of modern auto body "built in" crumple zone failures. Fortunately or unfortunately, lots of modern "totalled" wrecks head to the shredder within a few years of time in the junkyard......or "Auto Dimantler" operation.