Earlier quoted context omitted.
could have links to their diet Replace that with could have been caused by aliens to see how ridiculous that sort of claim is. There is no reason to suppose that dying under anesthesia is related to the diet. Also your analogy doesn't make any sense. Perhaps if they removed bikers that died in traffic accidents while not riding a bike . And then you could argue 'bikers behave differently in traffic, so perhaps biking…
I haven't read the studies. Still, why isn't it reasonable to think that a monkey that eats too little will die more readily under stress? You can remove clearly unrelated causes (e.g. monkeys run over by bicyclists), but it's not nearly so clear for anesthesia.
More importantly, deaths are just one of the variables being measured. The diet seems to improve quality of life, not just raw quantity. That's reason enough to be interested in these findings.
Furthermore, the author of this blog seems to doubt the role of Science in publishing these findings. The money they make has no bearing on the results. Other scientists, doing closely related work, reviewed the work in excruciating detail (read the footnotes, not the press releases) and found its clear scientific value. Sure, blame the media for the headlines. But the work, as a status report on the field, is very encouraging.