IIRC Stills was driving along and happened to notice Young's trademark '57 Cadillac hearse passing by in the other direction. (Young had used the hearse back east to haul his band's equipment around, at the time he and Stills first met each other. It was roomy enough to be an ideal band van, but it was actually more famous for breaking down on highways on the way to gigs.) Stills promptly turned around, caught up with Young, and the rest is history...
You, sir, are correct. My Neil mythology is a little fuzzy anymore. The hearse was called "Mortimer" and its demise was the basis of his song "Long May You Run." That song makes sense when you think of it being about a car that took him throughout much of his early career!