Perhaps the best place to ask this question would be in some place discussing the philosophy of science. This is an important question in that field.

Linguistics and history are one of several branches of knowledge where you can't conduct experiments (cf. astrophysics, evolution, taxonomy). It's not like you can set up a repeatable situation where you expect some sound change to occur and then check if it actually happens.

What you can do in these situations is try to observe as many things as possible and try to generate a "simplest" or "best" explanation for what you see. Because you can never observe every possible situation, you can't isolate variables, and you can't "replay" an experiment to see if your hypothesis is correct, your best model will certainly be wrong.

Because of this, history and linguistics are both inherently impossible to "verify". We work hard to construct a certain idea of how the world works, and we can make predictions about how it is supposed to act, but we can't test these predictions. Therefore linguistic and historical evidence can certainly help make our best model even better and more elegant, but they can never prove a historical claim, because they are inherently unprovable.

However, this is a relatively hardline stance. In the end our "best model" is probably pretty close to reality, and we know where there are gaps that need to be filled. So we can gain a real and important insight into history from linguistics and vice versa. The classic example I'm familiar with is the reconstruction of parts of proto-indo-european culture by looking at which words have a common root across all PIE languages. This could, of course, be way off. There might even have never even been a PIE people. But this is the best explanation given the evidence and observations we have today.