From this description, the mainstream view seems to subscribe to the discredited Lamarckian view of evolution, i.e. the idea that traits acquired during parents lifetime (e.g. bigger brains from eating meat) can be transmitted to offspring.
It's not that eating meat makes your brain grow bigger. It's (eating meat)/(eating cooked food)/(having a richer diet) that makes people born with a larger brain more likely to survive. Otherwise, a larger brain would be a hindrance since your body would use more resources than you could easily consume.
See http://en.wikipedia.org/wiki/Inheritance_of_acquired_charact...