Cooking food allowed for bigger brains in humans

This is the hypothesis that Richard Wrangham describes in his interview in this Scientific American article. This idea has been around for a while (see here, for example). The trouble has been establishing when hominins were able to "get fire". Some estimates point to as far back as 1.7 million years ago. In this interview, Richard Wrangham talks about the differences between chimp diets and human diets, and how modern day humans and hunter gatherers can't eat some of the fibrous, bitter, tough foods that chimps routinely rely on. He says that cooking food would have been the single greatest improvement in the quality of our diet - so he thinks that cooking would lead to a higher quality diet more so that just getting meat, or tubers, or nuts etc !!! This is the kind of hypothesis that is ripe (excuse the pun) for testing using genetics, as he mentions at the end of the interview when he talks about looking at genes involved in the Maillard reaction. I don't understand why he talks about using Homo erectus DNA though. First of all, that's not possible (yet?), and I think there are ways to answer a question like that just using modern human DNA, or by comparing humans to other primates.