Many U.S. Laws Govern Claims Made About Consumer Products
Are these claims governed by law?
The Lanham Act in the U.S., which primarily regulates federal trademark registration, also has a provision that allows competitors of a merchant who are harmed by false advertising claims of that merchant to sue the merchant in federal court.
The Federal Trade Commission also has broad consumer protection authority at the federal level that could be pertinent to this issue.
Most states also have consumer protection laws that prohibit merchants from making false claims that can be enforced by the attorney-general's office, consumers harmed by the false claims in ordinary civil actions, and in class action lawsuits. In California, whose consumer protection laws are particularly broad, a suit can be brought based upon the harm caused by the false advertisement itself, rather than merely based upon the harm that results from someone being actually mislead by the false advertisement.
In addition, misrepresentations regarding products causing harm to someone who buys the products can give rise to common law lawsuits for fraud or negligent misrepresentation, or under the Uniform Commercial Code which treats a representation made by a merchant about a product that the merchant is selling as an express warranty.
In some contexts, federal criminal charges for mail and wire fraud could also be brought.
There is also a large body of law governing "product liability" claims, but that governs situations where a product actually harms someone, not a situation where the product merely fails to live up to glowing statements made about it. So, it is unlikely that product liability claims would provide a remedy in this situation. In the same vein, the Consumer Product Safety Commission would probably not have jurisdiction over claims of false advertising related to a product that is not otherwise likely to cause physical harm when used as intended, even if it doesn't live up to representations made about the product.
Furthermore, if a firm with passive investors (even if the company is closely held rather than publicly held) did not adequately disclose to the investors that the firm was making false claims that it knew to be false to retail consumers, this would probably violate both state and federal securities law, both civil and criminal. If the investors lost money when this knowing lack of disclosure became clear, they would have securities fraud claims against the companies involved.
As to "the world" that is too broad a question for one answer. There are hundreds of countries in the world and an examination of all of their laws is simply too much.
When does the FDA step in, for example if the purpose of having a
"moisture-wicking" garment is to protect the wearer from catching a
cold after exercise, could this claim be part of the labeling?
FDA jurisdiction is primarily over food and drugs (as the name, the "Food and Drug Administration" suggests).
While FDA jurisdiction does extend also to "medical devices," it is unlikely that the FDA would consider claims related to ordinary clothing, even with allegedly premium fabrics which are claimed to have special properties, to fall under their jurisdiction.
The Center for Devices and Radiological Health (CDRH) is the branch of
the FDA responsible for the premarket approval of all medical devices,
as well as overseeing the manufacturing, performance and safety of
these devices. The definition of a medical device is given in the FD&C
Act, and it includes products from the simple toothbrush to complex
devices such as implantable neurostimulators. CDRH also oversees the
safety performance of non-medical devices that emit certain types of
electromagnetic radiation. Examples of CDRH-regulated devices include
cellular phones, airport baggage screening equipment, television
receivers, microwave ovens, tanning booths, and laser products.
CDRH regulatory powers include the authority to require certain
technical reports from the manufacturers or importers of regulated
products, to require that radiation-emitting products meet mandatory
safety performance standards, to declare regulated products defective,
and to order the recall of defective or noncompliant products. CDRH
also conducts limited amounts of direct product testing.
The FDA does not have jurisdiction over everything that is the subject of health claims, only food, drugs and medical devices.
For example, even if a jump rope advertisement claimed that jumping rope improves cardiovascular health and reduces obesity, this would not bring the jump rope under FDA jurisdiction. This is true even if the claims were false (e.g. "using a jump rope will cure Stage 4 pancreatic cancer in 9 out of 10 cases"). These claims might violated other laws, but the FDA would not have jurisdiction over these claims.
Do manufacturers only refrain from making more outlandish claims, like
the examples I gave above, because then people would stop being so
Manufacturers (or more accurately the people who market manufactured goods to the retail public, who are often not manufacturers themselves), generally do not make advertisements that they know to be provably false, but in the particular example that you cite of moisture-wicking fabrics, I do not believe that the people involved (who, after all, went into marketing because STEM wasn't their thing) believe these representations to be false, or have any inkling that they might be false.
I am not aware of any serious effort by any consumer protection oriented group to claim that these representations are false.
Could I sell a garment advertising that it wicks moisture into
outer-space, using technology developed by astronauts? While
protecting the wearer from plagues and earthquakes?
These claims would probably be interpreted as being made "in jest" rather than being made with an intent that they be believed and relied upon. There is no ban on obvious hyperbole or humor in commercial advertising.
And neutralizing armpit odor using anti-rot nano-particles?
I am pretty sure that there are products for which this claim is made. I have no reason to think that there is a belief on the part of the people making the claim that it is a false claim, or that anyone has established that these claims are false.
Are Claims To Be Moisture-Wicking Misleading?
I'm wondering why sports and outdoor equipment stores sell garments
that advertise themselves as "moisture-wicking" when clearly they are
made of wool or some synthetic material which, as far as I understand
it, is less absorbent and therefore less liable to act like a "wick"
via capillary action, than cotton, which is often a cheaper low-tech
alternative. Seemingly this advertising myth has become quite
entrenched in popular culture, I hear it cited by people all the time.
. . .
Also, many such garments additionally claim to "wick moisture away
from the skin" which would seem to imply some kind of violation of the
second law of thermodynamics or conservation of energy, or at least to
contradict the plain observation that the fabric is the same on the
inside and outside and contains no directional asymmetry.
This sounds like an ill founded and inaccurate assessment of the practical reality and relevant science, but this portion of the question really is beyond the scope of Law and more relevant to Skeptics.
In a lawsuit invoking some of the laws that I mentioned above, the allegation that these claims are misleading would have to be established by a preponderance of the evidence with expert testimony in a trial.
Also, in the context of commercial speech, while the First Amendment does not prohibit regulation of false statements, it does disfavor making courts the final adjudicator of claims when the reality is hotly disputed and no specialized expert regulator is reviewing the claims.
So, it would probably be sufficient to defeat a lawsuit alleging a misleading claim, to establish that legitimate authoritative sources with a scientific basis for their claims hold that the claim is accurate, even if other legitimate authoritative sources with a scientific basis for their claims disagree.
Normally, a court would not impose liability if there was a dispute of authority of this kind, unless their was a claim that experts unanimously agree that the claim is false (hence, advertisements in the form "9 out of 10 surveyed dentists agree that . . . ").