Hopefully, being a former claims investigator, I can offer some insight here.
This claim should be covered under COMP, in it's most general sense. That being said, MOST companies will not cover the CAUSE of the damage. An example would be if your tire blew out and you hit a guardrail. The insurance claim would cover everything that resulted from the loss except for the tire, being that it was "improper maintenance" that caused the loss.
Now COMP claims aren't usually logged on your record with liability being much of a factor, so don't worry when they tell you that it was your fault that the thing caught fire. Ultimately, it doesn't mean the same thing as causing a COLLISION.
Insurance companies tend to oversimplify things; as they are doing here. Those who have pointed out that your carrier can subrogate BMWNA are correct, although it will not get them anywhere. A good example of the only time those types of losses were recoverable after being paid were in the Toyota "unintended acceleration" debacles.
I cannot speak to the specifics of your policy, but the company I previously worked for would have paid for everything but the cause of the fire. That would mean a new or USED (and in comparable condition) seat and everything else. Of course, you will be responsible for your deductible, if you have one, and the module that allegedly caused the loss. Or you can take a check for the repair cost less those two amounts I just mentioned.
Ultimately, it was improper maintenance that caused this to occur. Now whether it should have happened is a different story, and I feel for you there.
To the poster who seemed surprised that the OP got in to his car to find his seat completely reclined; it's happened to me more than once. There are clearly some gremlins there...