So, your insurance says it isn't a claim since it wasn't due to damage, but Tesla still wants you to pay.
That is a tough situation. I think I would show up where my car was in person and have them physically show me exactly what was damaged and why they think it is not a warranty issue. Take photos.
If they insist there is evidence of collision damage, then I would probably file the insurance claim and let my insurance company duke it out with Tesla. Also, you are entitled to all removed parts if it is not a warranty repair, so I would insist on getting all of those as well. Then you might be able to have the failed part analyzed yourself to see if it was impact damage or some other cause.