Sam, welcome to the 'fest... and I think you misread my message.
Simply put; BMW will not make any statement until an investigation into the cause is complete. This is not hoping the problem will go away; it's simple Corporate legal crap that all corporations do. They don't want to say anything because to do so would be to commit themselves to an answer before all the facts were in. Even once all the facts were in, saying they will provide you any sort of resolution before legal has had a chance to weigh in (which could take weeks) is actually automatically going to be a falsehood on their part. Like it or not, corporations are run by lawyers.
Second, BMW isn't the ones who have to do anything here; the dealership replaced the parts, not BMW. BMW is not involved and all the dealerships are franchises and therefore not directly answerable to BMW.
Finally, truthfully this is an insurance issue now. Your insurance should cover replacement cost of the vehicle, and at that point they are responsible for the investigation into the cause. If they find the dealership is liable then you can partake of their lawsuit, file your own lawsuit or just choose to walk away. That's your call (though my non-professional advice would be to seek your own legal counsel for your own lawsuit).
I am glad no-one was hurt... and yes you went through a terrifying ordeal that I hope noone else does; but at the same time this really is between your insurance company and the dealer at this point. Even BMW is legally obliged not to get involved unless the investigation finds that the problem was a design or manufacturing flaw. I don't believe that there's a design flaw here because (a) we'd have heard about a lot more of these kinds of events and (b) a design or manufacturing flaw is most likely to come up soon after a vehicle is manufactured. Basically by the time a vehicle is a year old, manufacturing defects mostly will have worked themselves out... and design flaws... well they tend to come up a lot sooner. Considering how long your particular vehicle has been in production a design flaw seems unlikely.
I realize that in your current understandably emotional state you may be leery of BMW... I know I probably would be. But please understand I was merely trying to convey the fact that there is a process when stuff like this happens; first you get your insurance involved and they pay out for repair or replacement. It is then up to the insurance company to move on and attempt to find the root cause of the issue and then seek retribution from the party deemed responsible for the fire. Given the situation as I said, I would urge you to seek legal counsel regarding pain and suffering against the dealership... but understand that nothing will happen until the official investigation is complete.
You pay insurance on a vehicle for a reason; partly so that you have money to replace your lost goods (the car) and partly so that you can let them deal with the problems that come after (finding the responsible party, retribution, legal wranglings and so forth).
TL;DR: Seek legal counsel on whether you can file a lawsuit... leave the identification of the guilty party to your insurance company... buy a new car... hug your kids.
2001 E46 BMW 330i Sport Package 6MT
2004 BMW R1150GS
2004 E60 BMW 545i Sport 6MT
2012 BMW 135i - Deep Sea Blue / Terracotta / DCT
2012 BMW K1600GT - Vermillion Red Metallic
2008 BMW E90 M3 - Interlagos Blue / Silver / 6MT