Modern hunter gatherers are a lot more modern than one might imagine. Usually wearing T-shirts and sometimes, as in this case smoking cigarettes. Their diet is different in many ways than hunter gatherers of the past, along with many other parts of their lifestyle.
It’s probably a good demonstration of the “Paleo fantasy“- if these groups that are still playing by some of the hunter gatherer groups are getting very different results on these important markers, then we are likely to as well when we try to incorporate parts of the hunter gather diet or lifestyle into our very different lives.
Mostly fresh food- eating things they day they were picked or killed as the default. But generally in an environment of abundance with generational wisdom about what is nutrient dense. The group in the study may be eating lots of honey because they are more marginalized today by territorial pressure and others hunting and hunting restrictions, etc.