The claim "this medication produces this effect" is a separate claim from "this medication produces this effect via this process ". In those cases you mentioned, the first claim has enough evidence to reject the null hypothesis, and the second... well, if we don't know how it works, then we have yet to find such a claim that has rejected its null hypothesis.

For instance, aspirin works as a pain reliever. This has been shown with empirical evidence. However, if I said "aspirin relieves pain by infesting your blood with microscopic fairies who kiss your boo-boos from the inside out" -- that claim does not have enough evidence to reject the null hypothesis.