I also wonder whether someone living for a very long time wouldn't eventually suffer irreparable damage because of the radiation from the environment accumulating in the tissues. Nobody's claiming that we can survive, say, being thrown into a volcano (an active one, I mean), just by being more healthy and young. There are clearly environmental hazards that the body cannot withstand, senescence or no senescence. It is very likely that such environmental hazards hitherto unforseen will begin to reveal themselves once our lives are extended enough and that we will eventually find out that there is a hard upper limit for the amount of time that these frail bodies can keep serving for.
I clarify that this is not something to celebrate, or even accept. Let us not go gentle in to that good night, by all means. On the other hand I think it is ridiculous to believe that in a universe where galaxies die, human beings can keep going like the Duracell bunny for as long as we like, thanks to Nick Bostrom's Amazing Rejuvenating Pills™.