“You will need to inform your insurance company of the accident. While the other insurance company may want to work with your insurer, it doesn’t mean that you’ll be charged your deductible. When looking at claims, car insurance companies need to verify that someone is actually insured.
The other party’s insurance wants to verify your coverage before they settle a claim. This is completely normal—after all, you’re paying your own insurance company to protect you in a situation like this. You won’t be admitting any liability or fault by informing your insurance company that there was an accident.