While there are many experimental results that seem to align with the predictions of special relativity--some examples being muons from the upper atmosphere reaching the Earth's surface despite their short half lives as well as atomic clocks being flown in jets around the Earth reading different times than identical clocks left on the ground after the flight (i.e. Hafele-Keating experiment). My question is, how do we know that the results of these experiments (i.e. their disagreement with classical mechanics) are direct results of (and thus direct verifications) of special relativity rather than being caused by other unrelated effects such as decay rates varying with altitude and other external properties such as atmospheric pressure, or even with varying amounts of gravity (these are just some examples of ideas of other possible explanations that I had)? In addition, how do we know that these experimental variances from classical mechanics are caused by relative motion rather than gravity?
Essentially, how so we know that experimental results that seem to show special relativistic effects--such as time dilation or length contraction--due to relative motion can truly be directly attributed to special relativity? Do these experiments truly show (i.e. provide evidence for) the existence of special relativity or do they simply give the illusion of its existence due to other unrelated effects that give similar results?