Never really said otherwise, that's the same as most states. OP is entitled to pursue damages against the other driver. As to Enterprise, it can very reasonably argue that Enterprise did NOT grant permission to drive in New York State based on what we know of the rental agreement. If Enterprise denies coverage, it will take a court to decide. Although that gives the OP standing to sue them directly. If threatened, Enterprise might well decide to pay just to make it go away though.

Hopefully, Enterprise will do the right thing out of the gate. But they may have grounds not to and it depends on whether they decide to stand on them.

BTW, most states are like Canada in that third party liability coverage, stared simply, is generally required as part of the rental (without purchasing the various expensive waivers, regardless of how the rental agent might make it sound). However, insurance companies can deny coverage leaving the driver holding the bag if they violate certain of the express terms of the policy. For example, my own car insurance policies expressly state that person living at the the same address that is not declared as an "Additional Insured" will not be covered if driving the car, leaving me totally financially responsible if I let them. The same type of thing applies to self-insured car rental companies. It will depend on the language of the contract (the rental agreement) With that said, insurance companies generally rigidly enforce their policy provisions (and why it pays to actually read the policy). Rental car companies may be a bit more flexible to ensure a good image.