In the Human Brain, Size Really Isn’t Everything
nytimes.com
nytimes.com
The idea is appealing but I have no idea if its true.
Cooking food is an adaptive behavior that reduces disease and alters nutrition. It was the gradual exploitation of nature for the domestication of monocultural, industrial agriculture with supply chain processing that makes for most food modern people eat including "convenience" foods. This division of labor, whether organic farmer or pseudo-family megafarm, is what renders individual hunter-gathering a waste of time. From this over-abundance of calories and protein, it could support more robust bodies and larger brains, but it's a moot point considering obesity and the inevitability of the technological singularity.
http://www.ted.com/talks/suzana_herculano_houzel_what_is_so_...
The speaker argues that while there are animals with brains bigger than ours, their neuron density is lower; overall, humans have the highest number of neurons. She goes on by noting that the energy that the brain consumes depends only on the number of neurons, not the size, thus making humans the species that has the most energy-hungry brain. This leads to some interesting theories on how the evolution of our brain is related to our nutrition habits, which I found quite mindblowing.
But let's do a thought experiment and see if we can reasonably dispense with the need for experiment itself. The article (via the researchers' statements) zoomed past a detail: cortical surface area is much more indicative of neural processing capability than gross brain volume. In many contexts, a neuroscientist might use "brain size" as shorthand for cortical surface area. Also consider that more "advanced" mammals tend to have more convoluted cortexes, thus larger cortical surface areas. So it's quite possible for a large mammal's (whale's or elephant's) brain to be volumetrically larger than a human's, but to have relatively smaller surface area because it is less convoluted.
In the event that we could actually accomplish such a comparative study as you propose, we'd probably find that "tethering" does not monotonically increase with surface area. Then we'd determine that the authors' hypothesis is overly simplified.