It was used by Mitchell's daughter as a daily driver for a number of years, so I assume he offered it to her. From what I could gather, it then was used by the Reynolds family before it was discovered and restored.
Mitchell may have been referring to it in his interview with Dave Crippen in The Automobile in American Life and Society, The Automotive Oral Histories of The Henry Ford Museum:
Q: Why did he (Ed Cole) think the Corvair would go?
A: If it was here today, it'd be better than ever. It was economical, but what killed it, those were the days of dragster cars where you'd take, not just Corvettes, but you'd put big engines in the A bodies—all those Pontiacs and Olds that would rip the stones out of the street. Corvair couldn't do that. I built one for my daughter, and she was afraid to drive it, because you go to shoot across the street, and it wouldn't go, and even the blowers they put on acted like a slip and clutch. I built a couple cuties—the Monza, took 'en to Florida, six carburetors on it, a lot of fun; but the car wasn't timed right. Today, they're good looking. I got one for George Russell [former G.M. vice chairman], he's got it down in Palm Beach. He just told me the other night he's got it all restored. Good styling—is classic, it lasts forever.