Where does the poster say that she bought the car from a private party? Just because it was a used car does not mean that it was from a private party. I've bought used cars from dealerships. And under the link that YOU posted, she MUST be offered the 2-day cancellation for a used car, as well.
Two things I am tired of typing: 1.) A wrongful termination does not mean that you were fired for something you didn't do; it means that you were fired for a reason prohibited by law. 2.) The above answer, whatever it is, assumes that no legally binding contract or CBA expressly says otherwise. If it does, the terms of the contract apply.