On the LEF site (the first link I posted) there's a description of the various specific and measurable benefits of various high quality supplements, as established by various studies and published in respected medical, nutritional, and biochemical research journals.
That page has 182 separate citations. Click the "References" link to see all of them.
Those references are not enough for me to search for. I need article titles. (Edit: They also don't clearly mark which claims are associated with which reference.)
That site looks like its primary purpose is to sell products, not dispense genuine medical advice. As such, I view it with extreme skepticism. In more blunt terms, that product looks like modern snake-oil.
Also, "These statements have not been evaluated by the FDA. These products are not intended to diagnose, treat, cure or prevent any disease."
Well, you've stumbled upon some of the deep problems with nutrition information dispersal in the US. Many regard the FDA/USDA to be largely corrupt in their handling of health information, due to the many conflicts of interest and ties to pharmaceutical companies and food industry.
Making it illegal for farmers to label their beef as mad-cow tested is one example of this. The way trans fats are labeled in the US compared to Canada/EU is another example. In fact, in most of EU trans fats are not acceptable food ingredients. In the US, they're acceptable ingredients for vitamins. A third example might be the silence regarding the importance of sunlight and vitamin D as a prevention for many forms of cancer.
Regarding "these statements have been evaluated by the FDA" -- it's actually illegal for supplement companies to make anything that resembles a health claim about their own products, even if it's demonstratively true.
In general, the big problem with health information in the US (as you've demonstrated) is that it's inaccessible. There's plenty of industry and financial interest in it remaining inaccessible. So, you'll have to do more than glance at a website for 30 seconds and drawing the fast and easy conclusions.
Finally, the Life Extension Foundation is a non-profit with a 30 year history, and one of the most respected health and wellness research organizations world wide. Googling around will demonstrate this.
it's actually illegal for supplement companies to make anything that resembles a health claim about their own products, even if it's demonstratively true.
Absolutely false. It is completely legal to make the claim as long as you demonstrate that it's true to the FDA and they accept your data. If the benefit were actually present, they could file safety & efficacy data with the FDA and on approval legally make the claim. The fact that they don't tells me that there isn't any benefit worth noting.
That page has 182 separate citations. Click the "References" link to see all of them.