It is commonly stated: we cannot PROVE that any mechanism actually was followed.* Instead, we propose all of the possible mechanisms that we can think of, then we use experiments to try to DISPROVE them. In the end, we expect only one possible mechanism will remain, and this becomes the established mechanism.
But new data can upset things. You probably learned about SN1 and SN2. But did you know there is another second order mechanism (SNET) that is sometimes followed? It gives a few discrepancies from traditional SN2 that were overlooked at first.
So while there are well-established mechanisms that have stood the test of time, they might not actually be completely true.
*(This was more true back in the early days of mechanistic chemistry - now we have advanced techniques like scanning tunneling microscopy and time resolved x-ray crystallography where you might be able to see the atoms actually reacting. These can't always be applied, and often can't exactly replicate the reaction conditions. Also, although we observe one set of atoms following one mechanism, there are 10^23 individual reactions for a mole - is this truly the ONLY way they react? Or did we see a 1 in a million outlier? )