I think the grandparent meant "fundamentalism" as "mechanistic", and lots of things we can know (as you say using the scientific method) to be useful long before we have a good mechanistic explanation of how they work.
Some examples: aspirin (willow bark used for thousands of years, drug synthesized in 1897 and mechanism explained almost 100y later), or general anesthesia used again since mid 1800s and the mechanism is quite still debated.
This is not to downplay all the long term, or developmental, risks that using something novel can result in. But we can empirically know something about the effects without having good mechanistic models.
But it is usually not necessary for approval of a compound to be able to describe how it works on a molecular or cellular level. What you need to show are three things: efficacy, safety and quality, so basically: the compound has the intended clinical benefit, has an acceptable safety profile and can be produced with a consistent manufacturing quality. Most compounds fail because of lack of efficacy (roughly half), and roughly a third because of lack of acceptable safety.