Dietary fat and body fat are different things. Keto is associated with the former, but if anything it reduces the latter. I think his claim is that (excess) body fat is what makes you stupid.
I don't know what specifically this is supported by, but your objection is based on misunderstanding the claim.
Yes, body weigh fat, not fat. Your brain actually need fat. But obesity compromises the major organs. Organs the brain depends on. Less effective organs - e.g. heart and circulation - is going to compromise the brain.
First, it's kinda obvious. That is obesity compromises the organs. That would include your brain. Furthermore, the brain outsources a lot: blood, oxygen, glucose, etc. Obesity compromises the foundation the brain stands on.
