Here is even a review article that confirms this - review about Nootriment.com
I question the expertise of any site which promotes the use of oral GABA and 5-HTP for mood disorders. They lack a fundamental understanding of these, and I'm guessing of all the other things they sell.

No functioning brain is deficient in the amino acid GABA (gamma-aminobutyric acid) which is the main inhibitory neurotransmitter of the brain. It is a by-product of the Krebs/citric acid cycle that converts glucose to Adenosine triphosphate (ATP) the main energy source of brain cells (and most other cells of the body). As a result the brain is so awash with GABA that the blood-brain-barrier contains billions, perhaps trillions, of tiny molecular pumps1 to remove the excess into the blood stream for disposal.

What anxious brains lack is benzodiazepine binding sites on GABA receptors2 and the ones that exist are less sensitive. Trying to overcome this with more GABA is akin to trying to fix faulty spark plugs by overfilling the petrol tank. Plus the blood-brain barrier prevents orally taken GABA entering the brain. It will all end up down the 'S' bend.

As for 5-HTP, firstly the most serotonergic organ of the body isn't the brain, it is only a minor maker and user. The gut makes and uses about 95% of the body's serotonin. Almost all orally taken 5-HTP will be scavenged as soon as it enters the gut. The second issue is that antidepressants don't work by producing more serotonin. See my: Serotonin - The 'chemical imbalance' myth

Moreover, only about 3% of dietary 5-HTP is probably converted to serotonin. The other 97% is likely converted to protein, or kynurenine, the precursor of kynurenic and quinolinic acids. At least this is the case with l-Tryptophan the 5-HTP precursor.


[1]
Kakee A, Takanaga H, Terasaki T, et al (2001)
Efflux of a suppressive neurotransmitter, GABA, across the blood-brain barrier.
J Neurochem. Oct;79(1):110-8 [Abstract | Full text PDF]

Terasaki T, Hosoya K. (1999)
The blood-brain barrier efflux transporters as a detoxifying system for the brain.
Adv Drug Deliv Rev. 1999 Apr 5;36(2-3):195-209 [Abstract]

[2]
Hasler G, Nugent AC, Carlson PJ, et al. (2008)
Altered cerebral gamma-aminobutyric acid type A-benzodiazepine receptor binding in panic disorder determined by [11C]flumazenil positron emission tomography.
Arch Gen Psychiatry. Oct;65(10):1166-75 (Abstract)

Geuze E, van Berckel BN, Lammertsma AA, et al. (2007)
Reduced GABAA benzodiazepine receptor binding in veterans with post-traumatic stress disorder.
Mol Psychiatry. 2008 Jan;13(1):74-83 (Abstract)

Cameron OG, Huang GC, Nichols T, et al. (2007)
Reduced gamma-aminobutyric acid(A)-benzodiazepine binding sites in insular cortex of individuals with panic disorder.
Arch Gen Psychiatry. Jul;64(7):793-800. (Abstract)

Bremner JD, Innis RB, Southwick SM, et al. (2000)
"Decreased benzodiazepine receptor binding in prefrontal cortex in combat-related posttraumatic stress disorder."
Am J Psychiatry Jul; vol 157(7):1120-6 (Abstract)

Bremner JD, Innis RB, White T, et al (2000)
"SPECT [I-123]iomazenil measurement of the benzodiazepine receptor in panic disorder."
Biol Psychiatry Jan 15; vol 47(2):96-106 (Abstract)

Malizia AL. (1999)
"What do brain imaging studies tell us about anxiety disorders? "
J Psychopharmacol Dec; vol 13(4):372-8 (Abstract)

Morimoto K. 1999
Benzodiazepine receptor imaging in the brain: recent developments and clinical validity
Kaku Igaku. May;36(4):307-13. (Abstract)

Malizia AL, Cunningham VJ, Bell CJ, et al. (1998)
"Decreased brain GABA(A)-benzodiazepine receptor binding in panic disorder: preliminary results from a quantitative PET study."
Arch Gen Psychiatry Aug; vol 55(8):715-20 (Abstract)

Tokunaga M, Ida I, Higuchi T, Mikuni M. (1997)
"Alterations of benzodiazepine receptor binding potential in anxiety and somatoform disorders measured by 123I-iomazenil SPECT."
Radiat Med May-Jun; vol 15(3):163-9 (Abstract)

Uchiyama M, Sue H, Fukumitsu N, et al. (1997)
"Assessment of cerebral benzodiazepine receptor distribution in anxiety disorders by 123I-iomazenil-SPECT: comparison to cerebral perfusion scintigraphy by 123I-IMP."
Nippon Igaku Hoshasen Gakkai Zasshi Jan; vol 57(1):41-6 (Abstract)