The FDA is really trustworthy to the extent that they have good information. Science is always developing and changing. What the FDA might have thought was true 100 years ago might not be the advice today. But they have no incentives other than to keep the public safe. They do their best.
The FDA has had a shady history. The number one motivator of most people is money. The FDA can pretty much control how money is spent in the pharmaceutical industry. They have a history of blocking many natural drugs that would have little to no side-effects on the patients and fix many health problems in the United States. This makes the pharmaceutical companies more money and cause many health problems to the people with health problems in the United States.
In my view, the FDA has had a long history of acting in the best interests of the pharmaceutical industry, rather than in the best interests of the public. They have routinely approved drugs later found to be dangerous. The silencing of the whistleblowers is only the most recent event in a string of incidents that cast doubt on the FDA's trustworthiness.
No, the FDA is not trustworthy. The FDA is officially sworn to protect public health by assuring the safety and security of America's food supply, products, medicine and medical devices; make them safer, more effective and more affordable; and, provide the public with the information about food and medicine that they need to improve their health. And yet, despite numerous FDA regulations, death from adverse drug reactions is still one of the leading causes of death in the U.S., killing at least 106,000 yearly!