You'll always be my favourite devil's advocate - says Satan himself ;-)Devil's Advocate....
I can conceive of a scenario where pressing on the back of the screen, or pressing on something that is attached to the back of the screen, when the screen itself is fixed in place, is a force that could conceivably do damage. The edges of the screen are arguably the places you'd be most likely to do damage by pressing too hard, because the screen is only supported in the middle, the edges are free to bend and flex (and crack) depending on forces imparted on them.
Is it possible that damage was slowly being done over the course of 2 years, even microscopic twisting/bending forces, from pressing on the back of the screen in that area (i.e. pressing the button)? It's conceivable in my opinion. No one knows how hard you've been pressing on that button, or how hard the button needs to be pressed to function, including Tesla. Obviously any affected owner facing this kind of repair is just going to say that they only ever touched it with the faintest amount of force, whilst wearing soft padded gloves, etc. Few people are going to admit to doing this damage as they have a vested interest in getting the repair done under warranty.
I tend to agree that Tesla can simply say that repeatedly pressing on the back of the screen has - over time - cause internal damage that has ultimately caused this failure. The dispute over when the crack occured is a bit academic, I think, and would appear to be impossible to prove definitively.
I agree with @MrMoonUK in so much as that it is a lesson not to attach things to the back of the screen. This is a good rule of thumb generally for mods. They might not cause any damage, but if they do it's something Tesla can easily point to as being the cause - even if it isn't - and the reason they're not honouring the warranty on it. Sticking these buttons to inert, cheap bits of trim would be the sensible thing to do.
I hope you get it sorted but I think that your only hope in terms of small claims is if Tesla don't respond, which there is a good chance of to be honest.
FYI the offending clicker that can be actuated by pinkie pressure