This made me curious so I checked the FDA site. In case anyone else is interested:
From a very cursory review, it appears that health claims on the packaging are quite heavily regulated by the FDA[1], but advertising for dietary supplements and foods seems to fall outside their mandate and regulatory responsibility lies instead with the FTC:
"The Federal Trade Commission (FTC) regulates advertising, including infomercials, for dietary supplements and most other products sold to consumers. FDA works closely with FTC in this area, but FTC's work is directed by different laws."[2]
I'm not sure what's on the bottle, but presumably the websites falls under the jurisdiction of the FTC. A brief review of their site seems to indicate a far more relaxed approach is taken. For example:
"The FTC's standard for evaluating substantiation is sufficiently flexible to ensure that consumers have access to information about emerging areas of science"
"These factors are often weighed together to ensure that valuable product information is not withheld from consumers because the cost of developing substantiation is prohibitive"
"...the FTC gives great weight to accepted norms in the relevant fields of research and consults with experts from a wide variety of disciplines, including those with experience in botanicals and traditional medicines" [3]
I would read that as a medical claim, it doesn't matter if you quote another site or not.
The claim about stress seems to be based on experiments in rats and a single study with 12 participants.