Serious flaw with this video's reasoning:
If it were possible to be immortal, you'd probably need extremely good healing as a prerequisite. If your healing processes weren't excellent, eventually you'd shrivel up into an arthritic, forgetful, blind little mess of a human being, and forget being worried about losing all your limbs and eyes to random injuries.
It's kind of what tends to happen already to people that all the regular suspects fail to kill off, to some degree anyway. Disintegration by nearly invisible attrition. (Gee, that's not morbid at all, is it?)
(I wrote a post over here about the subject once, actually.)