I second HoVY’s points. The other point that should have made it into the title, in my opinion, is that medical interventions should target problems, not indicators of problems. (Your application of the idiom “don’t shoot the messenger” was especially clever, and I think you could have based the title around it.)
I was also impressed by your disentanglement of two additional means by which glycine prevents or lessens fevers, and your identification of this as a Gettier case, but I doubt that it belongs in the title.
I appreciate the general point about fooling ourselves into thinking that we know more than we do, and I have a supporting anecdote.
As a kid, I was a very gifted math student. Although I wasn’t averse to memorizing formulas, I always strove for understanding. Consequently, when I learned about Taylor series, I was shocked to realize that I’d spent the last three years mistakenly believing that I understood trig functions. It hadn’t really occurred to me, at least not since the early days of my algebra-2/trig class, that if I didn’t have the scientific calculator in front of me, then I’d have no way to evaluate trigonometric expressions such as sin(20), aside from the very rough estimate that it must be between 0 and 1⁄2.