Scalp-recorded EEG does not measure action potentials, it can only measure the graded potentials of basically one type of neuron (pyramidal cells) in the cortex, which is a really tiny percentage of both neurons and electrical activity in the brain. Additionally, there is also the various roles neurotransmitters play in the brain, etc., and glial cells seem to also play an important role. So, it’s definitely not the case that there aren’t any gaps that need new science, and even if there weren’t, it’s a pretty big stretch from there to decoding all brain activity solely through the electrical component.
You're probably right, but that doesn't mean GP is wrong, just that they need to state their thesis more carefully. There's more science to be done there, but there's no reason to believe that new fundamental laws of physics are required to explain the brain.