Q:

Transmission damage due to uneven tread wear on AWD vehicle

I have a 2013 Subaru Impreza with a continuously variable transmission with ~40k miles on it.  About two months ago I blew out the front right tire and took it to a tire shop.  The folks at the tire shop said the tire wasn't repairable and that I had to replace two tires.  The put the new tires on the back and moved the undamaged, but worn tires on the front.  I can't remember if the worn tires were 60% worn or 40% worn, but they were the stock tires that I bought the car with.
About a month ago (and maybe 2k miles after replacing the tires) I started hearing a humming/clicking noise from the car (though no indicator lights went off).  I took it to a shop and they told me that the noise was coming from the transmission and that I had to take it to the dealership.  The dealer told me that the transmission was shot due to the diameter difference between the worn front tires and the new rear tires.  Apparently the front tires are 4/32 thread and the rear are 10/32.  The dealer claims that the warranty (which covers the powertrain to 60k miles) is void because the tread difference was responsible for the error.  According to the dealer any tire shop should have seen the difference in tread and either changed all 4 tires or shaved the new tires down.  The dealership wants ~$10k to replace the transmission.
I know nothing about this stuff and have spent several hours reading through conflicting information trying to figure out whether the tread difference could shoot the transmission.  Based on some similar questions on this forum it sounds like the differential might be damaged as a result of something like this, but I have yet to see anything definitive about the transmission.  Assuming that the tread difference was indeed responsible for the transmission damage (and assuming that the transmission is really totally damaged) is it reasonable to ask the tire shop to help pay the 10k? 

A:

They likely do hold some liability, since they should have known that an AWD should have matching tire diameters across all tires.
They may argue that you hold some responsibility since the Impreza owners manual makes this pretty clear: . 

You must install
  four tires that are of the same size, circumference, construction,
  manufacturer, brand (tread pattern), degree of wear, speed symbol and
  load index. Mixing tires of different types, sizes or degrees of wear
  can result in damage to the vehicle’s power train. Use of different
  types or sizes of tires can also dangerously reduce controllability
  and braking performance and can lead to an accident.

However, it seems to be well known in the tire industry that AWD's  need matching tires, and that Subaru's tolerances are particularly tight:
http://www.souzastireservice.com/tires-101/tire-matching-awd-4wd.aspx

Subarus have, to our knowledge, the tightest tolerance of any AWD
  system. Since we see so many, we can tell you what the tolerance is.
  It can be stated in two ways: The first is 2/32nds tread depth across
  all four tires. The problem with this is that actual tire dimensions
  can vary from brand to brand and even from model to model.  
... 
You
  may ask what the big deal is? Well, on the Subarus, if all four tires
  aren't matched within 1/4" around the circumference, you will break
  the transmission, not maybe or sometimes - it definitely happens.

Here's a tire shop that took responsibility for installing mismatched tires and replaced a customer's differential:
http://www.weareaccurateautomotive.com/blog-0/bid/128677/Tires-for-All-Wheel-drive-vehicle-Beware (in this case it was due to a different tread design)

So to be clear, by replacing the two tires we reduced the circumference differential by .75" and the tread depth by 2/32nds.
  This is supposed to be good. The speed rating was identical, but the
  tread design was different.
We concluded that the tread design was the culprit. We replaced the
  transfer case and installed two more tires to match. Car fixed.

And here's another shop that ended up replacing a transfer case:
http://www.tirebusiness.com/article/19990705/ISSUE/307059999/matching-tires-on-4wds-differences-of-1-4-inche-in-diameter-can

Mr. Albert said he asked the customer: ``Why are you coming back to
  me? I put on the same sized tire that was on the vehicle.'' The
  customer replied that the auto dealership told him all four tires have
  to be the same height and should be the same brand.
Mr. Albert said he turned the invoice over to his insurance company
  which promptly reimbursed the customer and assured him his tire
  department had done nothing wrong. But from now on, Mr. Albert said,
  he's going to insist on installing only four identical tires on
  four-wheel- and all-wheel-drive vehicles.

So,  I'd definitely approach the shop and ask them to pay. If it's a national shop and the local manager won't accept responsibility, look up their corporate contact information and see if the corporate office will help out. Be civil and professional in your communications. If you have a local news media consumer advocate, get in touch with them since public exposure may prompt the company to do the right thing, likewise, you can try contacting them via social media. If all else fails, contact a lawyer about legal remedies.
That said, $10K sounds expensive for a transmission replacement... I would definitely shop around on this (and maybe go with a rebuilt transmission), especially if you end up paying for it yourself. I would have expected only the transfer case to need replacement, though maybe that's built into the transmission.

