I'd say they definitely shouldn't be trusted. For one thing there is some unnecessary red tape which slows down life saving research from reaching dying patients. We also have the fact that their red tape means it costs companies billions to bring a product to market. That cost means a monopoly of companies who can easily work together, are in charge of making effective medicine, with no incentive to truly create a revolutionary method, due to likely secret clause not to do that, such as how the cable companies used the government to create monopolies in different regions.
We also have the revolving door between government FDA employees and companies rewarding ones who were soft on them by giving them jobs, when their tenure is up at the FDA.
TLDR
This creates
1. Low competitions because the price to bring a drug to market is billions. This is why corporations paid politicians to put the FDA in place. To increase market share
2. Incentives for corruption based on the revolving door between FdA and drug company employees.
3. Slow processes that keep drugs from getting to market fast enough
This is simple to solve. You do it through the following.
1. Cut all unnecessary red tape and keep necessary redtape. Making it so life saving drugs can make it to market faster, and so it is cheaper to bring drugs to market, allowing more companies to attempt to do so, and advancing medicine at a faster exponential rate.
2. Stop the revolving door by making the FDA unable to hire anyone who has ever worked at a drug company