It would be very unlikely for you to end up on Hertz's DNR list because this is a franchise. It's essentially operated like a separate business from other corporate-owned Hertz entities.
Note that if you book at Hetrz.com this is disclosed in the terms and conditions at the time of booking:
If you decide not to purchase CDW, you may be required to provide a security deposit of €5,000.00 at the start of the rental using your credit card. If this amount is not available on your credit card, you will have to purchase Collision Damage Waiver (CDW) and Theft Protection (TP), or you may be refused a vehicle.
If you book a basic rate and do not take the cover products available at time of rental you understand that you are financially liable for the full value of the vehicle and related costs.
Reliance on an external policy or eligible credit card for coverage will require documentation that this cover is applicable for the Republic of Ireland. As these products are limited, to protect against shortfall in cover a €7 per day Supplementary Liability Waiver (SLW) charge will apply.
Customers declining CDW and TP are required to leave a pre-authorisation of € 5,000.00 on their credit card.
We strongly recommend that you fully understand the terms and conditions of any cover provided by your credit card company including your personal liability level and any impact on your private insurance before you decline any of our optional services.