First, the point of an extended warranty is to make profit for the owners of the company.  Their goal isn't to server the customer.  Having said that, I had an extended warranty on my 200 SS Camaro, that I owned a few years ago, and ended up having the transmission and rear end repaired under that warranty.  The dealership worked directly with warranty company and the only downside that I found was the fact that they were not reponsible to replace with new parts.  In my case, they tried to located a transmission in a car with similar mileage to swap out.  I don't think all the companies work the same.

I know pet warranties are almost always 3rd party meaning that the vet doesn't deal with the warranty company.  You submit your final bill and hope for a check.