Most vets do not directly accept or process pet health insurance at their office.
In most cases when you have pet health insurance you'll be billed by the vet and have to pay out of pocket for the vet bill and then be reimbursed by the pet health insurance for the cost of the vet visit.
So you can usually be billed and work with the vet especially if it's an emergency and then once the pet health insurance sends you the payment to pay the vet you can then pay the vet with that payment.
So unlike peoples health insurance where it pays the doctor or hospital directly the pet health insurance works differently and just gets reimbursed to you for the cost of the vet visit instead of paying the vet directly.
I've never known a vet to be able to accept pet health insurance directly but there might be a few that do although most health insurance for pets pays you back after you pay the vet first.