Originally Posted by
direwoof
With the state law, I wouldn't be charged insurance-wise, but I still think that, technically, Hertz could come after me. But I just can't find a source anywhere if this is true or just me worrying. Thank you for your help though

And my credit card actually would cover it I believe, but one of the terms is to reject the LDW that Hertz offers.

Yes, if you want to avail yourself of your credit card's free LDW coverage, you would have to decline the optional LDW coverage that Hertz offers.
As to third-party liability, if I am reading the Hertz website correctly, Hertz would not come after you for damages that were below the state minimum if you rented in NY or one of the few other states where Hertz provides the renter with primary liability coverage. (If Hertz could come after you for rentals in NY, it's hard to understand why Hertz would have special language for rentals commencing in NY and the few other states listed.)