Bad luck of cancer - or misinterpreted statistics?

A recent paper in Science (January 2015) claimed that the majority, 64% to be precise, of cancers is due to bad luck, so non-preventable. The message was spread quickly through media, including serious ones like BBC (and also radio Slovenia, if I may add). And while the paper has been criticized by many, the authors seem to stick to the original message.In this talk I'll give my view of the paper and try to defend a counter message that their analysis gives them absolutely no grounds to make such a claim. The arguments that I'll present have, to my knowledge, not appeared in published reactions to the paper. Obviously, if I am right, they are wrong, and vice versa. If I was Bayesian, I would, at present, give a 0.99 prior probability to the first option. Either way, it should be fun.