Thanks for that link.
Further to the idea of the brain being unaccessible to GABA (and its precursors):
It would be strange, from a biological viewpoint, if our bodies were not designed to extract the precursors to the major neurotransmitters that our brains depend upon to maintain normal functions. Of course we humans do extract what we need for that, by ingesting the amino acids in foods which are essential to the construction of neurotransmitters in the brain.
If none of them could make it to the brain, we would probably be slime at the bottom of the pond. We all get precursors to Dopamine, GABA, Serotonin, Acetylcholine and other neurotransmitters from foods. Many amino acids are termed "essential amino acids" because human life is dependent on them; we would all die without them.
Leaky gut is an issue in terms of the internal loss of precursors, it may disrupt uptake and absorption in ways both known and unknown.
The rather blase myth that ingested substances can't cross the Blood Brain barrier tends ignores the way alcohol (which is a neurotoxin) very definitely affects brain function and behaviour after ingestion, particularly in large amounts.
I can understand that many people have been taught the BB myth in a dogmatic way at school in the past and retain the idea. Teachers used to teach that the brain had a set number of cells at birth, that ingesting alcohol killed brain cells (that is partially true), and that "once they are gone, they are gone forever, you can't get any new ones". They were wrong, of course. The brain is adaptive and can grow new brain cells, and does so all the time. Dogmatism is understandable when science doesn't know any better, though the science moves on, and the old dogmas hang around for a long time after new discoveries.