Technically, the FDA doesn't approve or deny any supplements aside from general vitamins and minerals (those that have an RDA), they aren't "approved". If it was "FDA denied" (eg. contaminated product, bottles not containing the right product, etc), it's removed from the market and/or the company making it gets shuts down.
It's already happened a number of times... one of the biggest cases I can think of is when they banned Tryptophan for around a decade because of a contaminated batch that some people died from. It was banned that long because of misinformation that came up about it and partially from media coverage that spread that got some people thinking that it was the supplement, not the company.
With all that being said, there actually are watchgroups and organizations that do regulate supplements and regularly report to the FDA for any major adverse reactions (and the supplement companies that sell them are supposed to report these as well). The GMP (Good Manufacturing Practices) and USP (U.S. Pharmacopoeia) are the main quality assurance organizations (USP is for the U.S., GMP is for the U.S. and worldwide).
Also, as the others have said, there is a measure of personal responsibility, but it's not exactly the way they are saying. The best thing you can do when buying a supplement from a company is to call the company and ask them to prove their quality. No, not just ask if they have good quality, but ask them to prove it. Their products should be tested/reviewed by independent 3nd party companies to verify their quality and they should be able to prove it rather easily. If they can't prove it, I wouldn't use their products... it's your responsibility to know what you're buying and to make sure the company you're getting it from is good.
Good luck and I hope I helped!
Personal research in my role as a Product Specialist for a vitamin company