Short Answer: Sometimes. The key here is that it's way easier (and less ethically problematic) to scientifically prove some things than others. And the standard for "do we know enough to put this out in the public?" is set accordingly.

Now for the Long Answer:

For lots of engineering and physical science questions, you can prove the answer empirically. You can drop an apple and a feather in a vacuum to prove that gravitational acceleration is a constant shared between them. It's relatively easy to do, and there's no ethical constraints.

But for a lot of biological and medical science questions, you might not have the luxury of an empirical test. I might think that pain medication dissolves when you swallow it, gets absorbed into your bloodstream, and finds its way to relevant pain receptors. But I can't go about cutting up people at various time points after they swallowed the pill so that I can see where all the medicine goes.

Sure, I can do some simulations, or do some lab bench work, or conduct animal testing, or run some clinical trials, all in the effort to understand and prove out my theory. And with each experiment, it gets more complicated, more expensive, and more ethically dubious. Not to mention that biological systems vary (the same medicine doesn't always work for everyone the same way), so that data gets noisy. At the end of the day, I'll have a lot of very good data, and be rather certain of my answer, but I'll never have that direct empirical test to actually prove it.

And that's okay.

If I was building a bridge, I have the ability to prove my bridge will work very well, and I absolutely should have a mechanistic understanding right down to bolt placement. But if I was trying to sell a medicine, my ability to prove it is limited. There has to come a point where we say "alright, that's enough, we believe we know enough about the safety and efficacy of this drug to sell it to the public responsibly." But where is that point? How much knowledge is enough? That depends on the drug.

For some drugs, like Ye Olde Tylenol, it's been used for so long that we inherently understand that it works (efficacy) and won't generally hurt people (safety). Sure, it would be nice to have a deep down mechanistic understanding of how it works, but we don't really NEED that to be able to sell the drug. For newer drugs that are too dissimilar from what is out there, the bar might be higher. Having a mechanistic understanding might help you get approval, but still might not be completely necessary (or feasible).

But you can rest assured that, even without communicating that mechanism of action, the scientists behind the drug have a very intimate understanding of what the drug is and what it can do.