I think it's false. Hunter gatherer communities (no societies back there) lived by what they could find - either hunt animals or look for fruits, plants and mushrooms.
Then there was a shift towards agricultural societies, where people relied on their plantations and domesticated cattle. I don't think the cattle meat would be enough for most of their meals, probably the most of them would be bread and soup.
This is just a vague recollection from A Brief History of Humanity, but it makes sense to me. Eating just meat sounds terribly "costly", you have to actively ignore all other sources of food around you.
Even ancient hunter gatherers probably ate a diet of more (wild) plant than meat. Catching animals is hard work, with the technology of the time.
But in general, I think we know a lot less about the lives of people so long ago than many people (including academics) like to think. Research methods are often based on either assuming modern people's lifestyles are "just like" ancient people, or big leaps from extremely limited archeological evidence.
No, of course they didn't. They lived in the Ice Age. Edible veggies and nutrients were extremely sparse and hard to come by for 1M years. Also wild plants prior to cultivation were not these big beautiful tomatoes, apples, bananas, and cucumbers we see in the grocery stores today. Those plants were selectively bred for thousands of years to produce what you see today.
Grass-eating bison, aurochs, horses, goats, sheep, etc were our primary source of nutrition in the ice age, not to mention mammoths (as well as fish).
And this is evidenced by ancient cave paintings tens of thousands of years old depicting hunts as well as the bone remnants in the caves and homes of ancient humans.
But mostly what the conflicting theories with consensus that changes from generation to generation tells me is that it's very hard to know for sure how people 15K+ years ago lived.
Then there was a shift towards agricultural societies, where people relied on their plantations and domesticated cattle. I don't think the cattle meat would be enough for most of their meals, probably the most of them would be bread and soup.
This is just a vague recollection from A Brief History of Humanity, but it makes sense to me. Eating just meat sounds terribly "costly", you have to actively ignore all other sources of food around you.