Most Corvair fans will tell you it's not any more dangerous than any other 1960 car if you set it up right. (I'll elaborate later) The manual tells you specific tire pressures to run: 22psi in front, 32psi in back. That differential tire pressure is critical to compensate for the swingaxles and rear weight.
The problem was that this spec is different from other cars people were used to, and like today, no one read the manual. Especially mechanics. So you'd take it to a shop for something, they'd notice your front tires were a little low, and "fill" them up with air for you. And you didn't know.
I think there's some willful misinformation on both sides of this argument. There's a lawsuit between Chevrolet and National Highway Traffic Safety Admin that resolved in 1972 (3 years after the last Corvair was made) that settled saying that the 1963 Corvair (the one being tested) wasn't any worse than other small cars at the time.
Early Corvairs, however, have more and more safety features added in over the years. There's an early 1960 (mine) and a later 1960 model, and there were significant suspension changes between 1961, '62, '63, and '64. After that, the Corvair had a full redesign and was honestly a different car (still rear-engined, air cooled, unibody, but a different model). Each model year for early Corvairs the car was refined and made much better, so that '64s are really nice, pretty damn safe cars for the era.
I suspect the '60 definitely has some rollover issues if you drive it hard. "Spirited driving" was the term they used back in the day. I don't - I baby mine and keep it slow and easy. I'm not great with driving a manual yet anyway.