Now it is true that when you sign an insurance policy, part of the contract makes the insurance company liable for the driver if he is in an accident in another vehicle and for whatever reason there isn't a primary or the primary uses subrogation to recoup damages from that insurer.
But that is not the most common case, and certainly shouldn't be used as the standard for what to expect would happen in this case.
Have you ever heard that women's insurance rates are typically more expensive than men's because they lend their cars more often to others? Now why would that be if the drivers were responsible as opposed to the vehicle insurer? Again, civil law is not black and white. Insurance companies have teams of lawyers in every major city in the country to fight their way out of claims when possible and certainly there are times that they succeed in recouping some damages from other insurers. My point was that this is not the norm. The primary insurance company is the first in line when a claim is to be made.