I'm not sure I buy it myself, but it seems used for "borderline, OMG super-dark" heroes a lot.
Personally, I agree with you that Jason is consistent in both, BUT I have always felt that Jason made a clear decision on that balcony and probably did push (or kick) him. In the conversation on the original s_d, I was in the minority though, which actually has made more intrigued and semi-critical of some of the later Jason stories.
And as for the "had Jason survived" question, I think so and I think Dini's Countdown (excuse me *gag*) answers that for us a bit. In one of the few alternate universes where Jason DOES survive, he becomes super commited to the cause and eventually becomes the next Batman. So survey says, YES he doesn't have to go off the deep-end! Would be interesting to have an entire AU comic to see how that transformation happened... except that no one likes Jason or AUs that much. ;)