I was a claims adjuster for 18 years, so this is simply my experience speaking. I can tell you that it would likely go as follows:

As a general rule, insurance follows the car. Therefore, the limits that Hertz has to buy on each of their vehicles will follow, and cover you for THIRD PARTY LIABILITY AND PROPERTY DAMAGE. Note that, especially in the U.S. (not so much in Canada, and I'm not certain in Europe and RTW), you will likely get sued for more than the limits of the Hertz policy, so you need to ensure that you are covered elsewhere. Most insurers will allow you to add non-owned automobiles that you rent short term for a very nominal fee. Check with your broker or agent.

When the collision happens:

1. If you are not at fault, there should be no issue.
2. If you are at fault, the following will occur:
a. Hertz and/or their insurer will negotiate and settle with the third party for the property damage to their vehicle (no-fault pd jurisdictions excepted).
b. Hertz and/or their insurer will negotiate and settle with the third party for any bodily injury claims (no-fault PIP/Accident Benefits jurisdictions excepted).
c. Hertz will negotiate and settle with any passengers in your vehicle for their injury claims (no-fault PIP/Accident Benefits jurisdictions excepted).

Now, after that occurs:

1. If another driver is not listed, you will be in violation of the contract. Hertz would then have a contractural action against you for any and all damages paid.
2. Hertz could also say that, as you were in violation of the contract, injuries you sustained as a passenger are non-compensable. This is dependent on the jurisdiction that you are in.

The long and short is to make sure you use a credit card that provides coverage, or that you have coverage through your home or work auto policy. I know many people that rent vehicles that have an agreement with their employer to pay the $300 (or whatever) annual fee on their gold card in lieu of taking the extra insurance.

Your mileage may vary. I am again only speaking from experience.