I believe the fundamental error in your thinking is that you hypothesize any possible time of death is that person's "time". Think of this: My walk to the grocery store takes me along a busy street (Hastings) as it enters a busy highway. If I chose suddenly to jump out into traffic and be struck by a bus, it doesn't change the fact that my time could have kept going if I hadn't chosen to jump out into traffic. There are infinite possibilities for death every day, and the likelihood of those events are independent of eachother. So by you not choosing to wear your seatbelt, simply deny yourself further life, possibly ended by some other randomly occurring death. Why not simply take measures to enhance life... are you truly that eager to meet your death?
You're asking, what rational person WOULD jump out into traffic on a whim and end their life? I point you to the Stoics of the ancient Roman empire who held suicide as man's highest measure of freedom of choice. Certainly there are still people around today who hold this. For instance, what was the motivation behind
Suicide Club. Now as you proposed earlier, we aren't discounting statistically improbable elements in our hypothesis. If you're allowed to have your life experience, I'm allowed to have past life experience.
Just an alternate viewpoint.
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God I got a good chuckle about remembering the time I watched Suicide Club... what a fantastically ridiculous movie. It made no sense what so ever.