Whether that specifically is speculation or not, it is a fact that we have adapted to live off of both meat and plants, and are some of the best known generalists (in terms of adaptation), among large land-dwelling animals. Other apes are much better at specific things that help them do what they do (specialists). We're just different, and we gradually became to be that way. There are specially adapted humans as well, less-speculatively as a result of rare rich protein sources like fish, milk. By extension, it's also probably inarguable that certain groups of people would have disappeared completely had it not been for the capability of them to adapt, bioculturally, to a changing world or simply changing circumstances. By saying their claim about meat and big brains is "Complete and utter speculation", you're at least implying that there's very little substance to the claim, and that you have a better explanation with more than a documentary to point to. But why is it that we're not competing with other apes at this moment? Why are we well-adapted to eat animals? Do you have a more substantial proposition?