Correct for non-Rx over-the-counter drugs.
The FDA requires proof of efficacy for Rx drugs. The FDA can withhold approval for a drug even if it does have efficacy, if there are already another drug on the market to treat the same conditions and has about the same results. Also, the FDA can unilaterally decide whether a drug is Rx or over-the-counter. Despite what many believe, this is not how it works in some countries outside the USA, where the emphasis is do no harm, rather than require proof of efficacy (which can cost tens of millions of dollars for clinical trials and take years to accomplish).
For non-Rx over-the-counter drugs the FTC (Federal Trade Commission) requires that all advertising claims be truthful, just like any other product. However, they rely heavily on opinions from the FDA as whether a drug has proven efficacy, usually as demonstrated in a randomized placebo-controlled clinical trial. So even if some doctors recommend certain vitamins and supplements to help with certain conditions, the FTC can still ban any claims that the manufacturer or retailer makes about them.