For one thing, it's considered "wear and tear" and the dealer will think that you didn't take good care of it. You can't get away with everything! Yes they may believe you but they will definitely not budge in. For one thing, as i mentioned, YOU ARE OUT OF WARRANTY so anything beyond that is just useless. Plus, as you did mention, it is a $3k+ thing, so definitely it won't fly with the dealers. I remember my dad broke the coat hanger in my GX, and the dealer replaced it (well it was in warranty) for free BUT that was OUR fault, and not a defective part. IT was a cheap thing so dealer will replace it w/o any questions.
Go ahead and try other dealers (cuz no one can really stop you) but they will say the same. I mentioned here before that my dealer scratched up my rim, but it took me forever to get the dealer to retouch my rim. It wasnt a regular scratch, but a "graffiti" like lettering (an L and F on my left front rim) but at first they wouldn't budge in. Definitely, not my fault because i dont write on my rims!