However, their history is very cool: when the Spaniards were enslaving everyone they could catch in northern Mexico for a short and harsh life in silver mines, the Tarahumara did not like what they saw, and headed for remote areas.
This would explain "the secret of longevity and perpetual health" - quite literal survivorship bias.
The Tarahumara are not very hygienic to even modern day indigenous standards. They are not very cleanly and the washing of their clothes is usually either an annual or semiannual tradition. The Tarahumara have no regular sleeping habits and simply go to sleep whenever and wherever they are tired and feel that they need rest. The practice of childbirth is also distinct to the Tarahumara. When a woman feels that it is about time for her to deliver the baby she will go off by herself into the wilderness, brace herself between two small trees and attempts to have the baby safely. There is a very high infant mortality rate among the Tarahumara. This fact is counterbalanced by the fact that there is also a very high birth rate. The average Tarahumara woman gives birth to about ten babies hoping that three or four will survive into adulthood. Adulthood is usually short for the Tarahumara with the average life expectancy being forty-five (Lutz 50). These factors are believed to help the Tarahumara survive as a race.
Perhaps the reason they have low incidence of diabetes, cancer, and heart disease is that these ailments often set in after the age of 45?
"Life expectancy is heavily dependent on the criteria used to select the group. For example, in countries with high infant mortality rates, the life expectancy at birth is highly sensitive to the rate of death in the first few years of life. In these cases, another measure such as life expectancy at age 5 (e5) can be used to exclude the effects of infant mortality to provide a simple measure of overall mortality rates other than in early childhood."
One guy getting in a better shape after diet and exercise is quite expected.
Whole society being virtually free of big bad diseases is, on the other hand, extraordinary claim:
"When it comes to the top 10 health risks facing American men, the Tarahumara are practically immortal: Their incidence rate is at or near zero in just about every category, including diabetes, vascular disease, and colorectal cancer."
This sounds quite dishonest if what mark_l_watson said indeed holds. You could then equally say:
"When it comes to #1 health risk facing Tarahumara men, Americans are practically immortal: almost all their babies survive."