No, I don't think you do understand. Or else I'm not understanding you.
Active ingredients are approved for very specific claims within precise concentration ranges. The FDA even specifies what words can go on the label. If they say a particular concentration of menthol allows you to put on the label that your product "helps relieve pain associated with common backache", then you're not allowed to get creative and write, for instance, "stops back pain" instead.
If there is no FDA approval for particular claims related to an ingredient at the concentration it's in, then it's not an active ingredient, no matter what it may actually do.
As far as sulfuric acid goes, you're not going to be allowed to put that in a topical application, so it will not be any kind of ingredient, active or inactive.
Well, since there's no concentration provided for the "inactive ingredients" of HeadOn, I remain skeptical. Menthol is listed as an "active ingredient" in products with as little as 2% concentration (cold creams, mixed with camphor and eucalyptus oils). It is evidently safe, but my point is that it is listed as "inactive" here and "active" in other applications. I doubt its chemical properties vary based on the label... I was being facetious about the sulfuric acid.
By the way, here is the full listing of the "Inactive Ingredients" in the order they are listed, along with a brief description. Somebody mentioned that these would be in homeopathic quantities, but that only applies to the
active ingredients. Assuming that HeadOn complies with FDA standards for active and inactive ingredients, it's ironic that the active ingredients do nothing whatsoever in the (non)quantities provided, but several of the inactive ingredients could have measurable effects, some of them negative. Also, please note that none of these products are uncommon in products such as cosmetics, despite the fact that some appear to be potential neurotoxins and carcinogens. There is a rather alarming lack of research and knowledge about some of these chemicals.
Diazolidinyl Urea:
Used as a formaldehyde-releasing preservative in cosmetics and barrier creams. It can cause mild allergic reactions, such as dermatitis.
Ethyl Alcohol:
The same alcohol found in beverages. Harmless when used externally, though it is flammable.
Iodopropynyl Butylcarbamate:
Used as a broad spectrum biocide or preservative to inhibit the growth of microorganisms. It is used a poisoning agent in insecticide, and is considered highly toxic to humans. It is suspected of neurotoxicity, liver/gastrointestinal toxicity, and reproductive/developmental toxicity.
Menthol:
A mild local anesthetic and counterirritant that is found naturally in peppermint oil. It triggers cold sensors on the skin or mucous membranes, giving a cooling sensation without an actual drop in temperature.
Menthyl Lactate:
A flavoring agent that provides a light minty odor/taste. It is commonly found in skin cleansers and denture adhesives, and appears to be quite safe.
Propylene Glycol:
Numerous applications as a flavoring agent and moisturizer, it is also used (in high concentrations) as the main ingredient in automotive and aircraft engine coolant. It is recognized as safe for use in food and cosmetics.
Sodium Stearate:
Soap. Safe for external use.
Steareth-21:
Steareth is an emulsifier. The number indicates liquidity (4=liquid to 100=solid). It is assumed to be safe based on similar chemicals.
Tetrasodium EDTA:
A "penetration enhancer". It allows other chemicals to more easily penetrate the skin, increasing their concetration in the bloodstream. Not harmful on its own, but can provide an access route for toxins that typically would not penetrate the skin.
Triethanolamine:
A pH balancer, used to reduce the acidity of cosmetics. It is suspected to be a carcinogen (insufficient research to confirm for certain), and it also increases skin and lung sensitivity, which can cause allergic reactions and asthma attacks.
Water:
What would a homeopathic solution be without water? Answer: nothing at all.