>New York is a no fault state
>Joe sues Bob's insurer
I don't think that's how no-fault works. You (and your occupants) are covered by your insurance company. The other person's damages/injuries are covered by theirs. Regardless of who was at fault (hence 'no fault'). One company suing another is restricted and rare.
Needless to say, (((lawyers))) don't like this system.