"There may be a deeper process at work here which accounts for the correlation of brain activity and thoughts that doesn’t necessitate one being caused by the other."
But whatever that deeper process is it will be related to the physical, biological and chemical components of the brain because if you take away the brain there is no thought or consciousness.
Consciousness is not separate from the brain. The relationship between the physical, biological and chemical makeup of the brain and "thoughts" or consciousness are clearly not understood fully but you cannot separate that process from out with the brain, its matter, its chemical and biological processes either.