But I wouldn't dismiss the possibility that humans are natural herbivores. I'm just not convinced. And I don't really care, except that I think when vegans assert that we are herbivores as a bald fact, they are opening veganism to attack. Why should we hinge our philosophy on scientific theories that have not yet been proven? Why should we hinge our philosophy on scientific theories at all, since even "proven" scientific theories can be found false at later points in history?
I totally agree with your comment that the dietary habits of apes, chimpanzees, and other primates is irrelevant to the question of what humans have been eating for the past 150,000 years.
But there is a lot of variation in meat intake of different omnivorous species, and I'm sure that species that only eat very small amounts (like the 5% insects you mentioned above) would get sick by eating more, so showing that an omnivorous species gets sick when consuming large amounts of meat does not prove that they are naturally herbivorous either.
Edited to Add: If a person has a cat who gets sick on conventional cat food (full of hormones and antiobiotics from franken-animals) and then gets well eating vegan food, it doesn't prove that cats are herbivores.