Hunter-Gatherer Wiki
Can't find too many good references, as most of what I say next came from a few papers / reserach gathered in a few Archeology classes.
Hunter / Gatherer societities were typically unable to survive based on Hunting vs gathering, meaning, they really didn't Hunt / consume meats as much as is implied.
The energy to be able to track, hunt, kill, drag back, clean and finally consume was to high to make this a feasible day-to-day (especially eating meat 2-5x a day?) diet.
Most of the Hunter Gatherer societies were really just Gatherer, with a smattering of "luxury" meats.