That fails to explain those who attempt suicide more than once.
EDIT: I found an informal estimate from this article (http://slatestarcodex.com/2013/04/25/in-defense-of-psych-tre...) by psychiatrist Scott Alexander:
"It is somewhat harder to find good studies on what percent attempt suicide again. By eyeballing some other statistics and trying to fit them together, I believe it is greater than 25% but less than 50%. One textbook whose studies I have not been able to verify says that 30% of untreated and 15% of treated suicide attempters try again."
This reminds me a bit of that movie "Strange Days" (where people relived others' experiences), or of course "The Matrix".
It seems, at first thought, unreasonable that people trying to kill themselves by jumping off a bridge would be more likely to regret the decision than people who shoot themselves in the head. I wonder if this is mostly a selective choosing of the survivors of jumping off the bridge to fit a narrative.
I do recall one man who did not survive, who seemed at peace during the video of his fall -- he was one who I think perhaps did not regret the act, but was the extreme outlier in that regard. If you are 85 and dying of painful cancer, I can also see it being an act that makes sense, made to decide one's own fate. But MOST people seem to grow out of their suicidal phases, and realize it was the wrong choice, driven by bad thought patterns. In the same way that people try to help addicts or people with eating disorders try to obtain better thought patterns, suicidal ideation seems to me to be largely a broken thought pattern we should help people overcome, not an individual decision one should respect.