They also smoke a lot less, but they do get more infections which could potentially increase the risk of heart problems by causing inflammation in the body.
One idea is that intestinal worms - which dampen immune reactions - could be more common and this may help protect the heart.
What can I learn?
Prof Gurven said: "I would say we need a more holistic approach to physical exercise rather than just at the weekend.
"Bicycle to work, take the stairs, write your story on a treadmill desk." (I didn't)
Dr Thomas said: "It could be to maintain health we need to be exercising much more than we do.
"The modern world is keeping us alive, but urbanisation and the specialisation of the labour force could be new risk factors [for an unhealthy heart].
"They also live in small communities, life is very social and they maintain a positive outlook."
What do experts make of all this?
Dr Gavin Sandercock, reader in clinical physiology (cardiology) at the University of Essex, said: "This is an excellent study with unique findings.
"The Tsimane get 72% of their energy from carbohydrates.
"The fact that they have the best indicators of cardiovascular health ever reported is the exact opposite to many recent suggestions that carbohydrates are unhealthy."
Prof Naveed Sattar, from the University of Glasgow, said: "This is a beautiful real life study which reaffirms all we understand about preventing heart disease.
"Simply put, eating a healthy diet very low in saturated fat and full of unprocessed products, not smoking and being active life long, is associated with the lowest risk of having furring up of blood vessels."