Given that, I don't think it is that bizarre that people might have developed a general mistrust of these agencies.
Of course you're conveniently leaving out all of the people who have died from FDA wrongdoing, and government wrongdoing in general.
The fact is that around 1 in 3 Americans die from drug use or drug-related causes. When you put it that way it doesn't sound like the FDA is such a trustworthy agency, does it?
Likewise, opiates kill a lot of people. But how many people would forgo life-saving surgery because of the pain they would have to live with after the surgery if effective painkillers were illegal? My guess is a lot more than the number of people who are killed by opiates directly.
The duty of the FDA is to make sure that drugs are safe and effective. If they're overpermissive, more people will die of drugs themselves. If they're too restrictive, people won't get the medicine they need to stay alive. It's a tricky balance to strike, and I think the FDA is doing a reasonably good job.
People dying from drug abuse is largely the government's fault, and relatively few people die from taking drugs that are medically necessary.
Also, I'm fairly confident that drugs being illegal causes fewer people to die from drug use directly.[1] Drug illegality makes drugs more expensive, which makes it more difficult for the average junkie to obtain a lethal dose.
Another big issue is medical errors. This isn't a government problem so much as it's a problem with our health care system. I'm not really sure whether government-run healthcare would improve this (by removing the profit motive to see as many patients as possible) or make it worse, by creating the wrong incentives.
It's really easy to blame the government for everyone's problems, but government regulation often saves lives, even if it ends up indirectly killing some people. For example, if the FDA kills people by prohibiting a potentially life-saving drug for safety reasons, they look really bad. But you don't see the people whose lives were saved because they didn't take a drug that turned out to be severe latent carcinogens.
[1] Of course, drugs being illegal makes more people die from drug-related violence. Violence is probably a worse problem, even if it's less deadly than overdosing, because it can affect nonusers.
Cite, and cross-reference to deaths avoided/delayed by use of same drugs.
And are you really claiming that smoking cigarrettes is saving hundreds of thousands of American lives each year?
Thought by whom? There are plenty of chemical carcinogens in cigarettes that are undoubtedly playing a role.
Smallpox - eradicated from the face of the earth (barring lab samples).
Polio - only 50 years ago, there were tens of thousands of cases in the U.S. Ten years later, after a serious vaccination push, it was down to a bit over a hundred cases. 1979 - last indigenous Polio transmission in the U.S. (globally, it just won't die, in large part thanks to the efforts of religious fruit-loops convincing people it's a plot by the U.S. to sterilise them; we pushed it more or less down to a single country, and now heart-breakingly it's spreading from there again).
Whooping cough - beaten down from tens of thousands of deaths to dozens in the U.S., and then cases started rising again when people stopped having their children vaccinated at the start of the 21st century.
The list of diseases that no longer present a real daily threat to people goes on and on. Let's have someone big from the relevant government agency on the news telling people that they're killing children by dodging vaccinations.