I don't think this is the whole truth or even correct. Other sources say otherwise:

http://www.cfspages.com/chelation.html
"Glutathione should always be the first chelating agent to consider as it is the body's natural chelating agent. Indeed, it is beleived that a breakdown in the body's glutathione stores, synthesis and reclamation are a prerequisite to developing mercury toxicity. Glutathione (GSH) in the blood directly binds inorganic mercury (Hg2+) in a 2:1 ratio of GSH-Hg-GSH. This complex is seperated from the blood cells along with the rest of the water soluble contents of plasma at the kidney via glomerular
filtration."

http://www.cfspages.com/nutrition.html
"Mercury inhibits the synthesis of glutathione, and depletes glutathione, a very important compound used by the body for excreting mercury, immune function, and protecting many chemical functions in the body."

http://curezone.com/blogs/fm.asp?i=969389
"Glutathione deficiency has been found to be virtually universal in
autoimmune diseases. This deficiency has two major implications: detox failure and viral/microbial activation. Glutathione plays a major role in detoxification. This deficiency impairs the body's ability to get rid of toxins."

http://www.glutathione-gsh.com/autism.html
"Glutathione's ability to chelate toxins"

Note the words used: glutathione detoxes, excretes, chelates mercury. And Andy is telling that glutathione is not a mercury chelator? Glutathione is the body's natural way of dealing with mercury. Claiming that glutathione does not chelate mercury is the same as saying that our bodies are unable to deal with mercury on its own, which is just false. Any other chelator does the same thing as glutathione, it can just bind to mercury, but whether this compound is excreted or just hangs around is another matter. It also meets the stricter requirement of having two bonds with mercury, but it is done with two GSH atoms that binds to one mercury atom.

Whether orally given glutathione actually works, depends on its ability to penetrate into the cells, where it is needed. This appears to not be the case for usual glutathione. However, newer formulations of glutathione, such as the liposomal glutathione appears to solve this problem to some degree, and you could then call even orally given glutathione as a true chelator. Also the efficiency of alpha lipoic acid may be mostly because of its effect to raise glutathione within cells.