It's not just a theory. Many animals have bigger brains than humans including mammoths.

The Neanderthals and earlier Homo Sapiens Sapiens (which have had larger brain than ours too), have had smaller bodies with larger brains though.

Actually, intelligence is a hindrance, not help when fighting a lion. I mean, it's useful to have one smart person in the tribe, to invent all those weapons, but smart people tend to overthink everything, making them worse fighters/hunters.

This is absurd. The only reason modern humans overthink things is because the modern environment and conveniences do not really challenge humans in the same way they evolved to be challenged. A group of male humans is excellently evolved to fight a lion or a mammoth or another group of male humans, and in doing so, execute complex strategies and tactics as a team.