The paper is available at
http://www.pnas.org/content/early/2017/10/25/1618854114
I'm not sure I can follow the math, but as presented in the article posted, the explanation doesn't really persuade me. They seem to explain it as a conflict of two opposing factors, some cells slowing down and losing function vs. others accelerating and proliferating eventually becoming a Cancer, so defending against one necessarily promotes the other. Then again there are other multi-cellular organisms that live longer than us [1] which should serve as evidence that there are ways to live that much longer
[1] http://www.bbc.com/news/science-environment-37047168