Yikes! That's a scary conspiracy theory!
(Note that I don't agree it would cause a breakdown in society.)
My comment comes across as semantic nitpicking, but I don't mean it that way; I just think I'm not understanding what you mean by reasoning "by induction" here.
I am a mathematician, so am most familiar with induction in its technical mathematical sense, which I assume isn't what you mean. More generally, my dictionary says that induction is "the inference of a general law from particular instances". For that to be what you mean here, you would need to infer that "someone makes sure they don't" (meaning, I assume, "they don't succeed in curing death by aging") in general from the fact that someone has done so in particular cases. Is that what you meant? If so, who and when? Or is my dictionary wrong, or are you using some other sense of 'induction'?