Even if you're right, that doesn't explain if I'm on the hook (and for how much) or if the signer on the rental agreement is liable?
I'm not particularly familiar with rentals in Israel, but let me explain how it generally works.
When renting a car the rental agency requires a cc on file. Reason being that in case you damage the vehicle and
A) You didn't buy insurance from the agency
B) Your cc CDW isn't covering due to any one of many reasons
they will be able to bill you without worrying that you can't pay - they just bill all the charges to the cc on file.
With that said, let me try to answer your questions.
In order for the cc's CDW to cover the rental, the name on the cc must match the
primary renters name listed on the contract. If it matches, it will cover all additional drivers listed on the contract as well.
The also applies to AU credit cards. If the AU uses his card and he is the primary renter, it will cover.
Regarding the rental agency, (in a scenario where insurance doesn't cover) they will bill the cc on file for the damages wether or not it matches the name on the contract.
Does this answer any/all of your questions?