Nature published this year the following paper: Evidence for a limit to human lifespan1, in which the authors argue their "results strongly suggest that the maximum lifespan of humans is fixed and subject to natural constraints."
One of this paper's statistical analysis has been panned at some sites already, including Nature article is wrong about 115 year limit on human lifespan and Evidence for a limit to effective peer review, since it turned up in some popular media.
The study is based, among several things, on data from databases detailing the yearly maximum age of death. Among their analyses, the following figure is included:
Basically the authors argue there's a breakpoint, and so they performed a segmented regression before circa 1995 and after that point onward. The regression is used as evidence for the limit of human lifespan.
Does it make sense though? If not, what method could better be employed to study these data?