The way I heard this story is that the movie being saved wasn't actually the theatrical Toy Story 2. Instead, it was Disney's version that was mostly scrapped when they resolved their dispute with Pixar.
And then, some months later, Pixar rewrote the film from almost the ground up, and we made Toy Story 2 again. That rewritten film was the one you saw in theatres and that you can watch now on Blu-Ray.