Where did you book the car hire? Usually if it's through a UK website, then it comes as a package with most of the basic insurances included, including loss or damage waiver (although with an excess usually) and third-party liability cover. These usually can't be removed/declined as it is considered part of the package. Now they will then try to sell you the next level of cover up, which normally has things like removal of any excesses, personal effects insurance, additional drivers etc. and these CAN be declined.
However if you've hired the car through a US site, then normally it doesn't come with any insurance as standard (although once again they will try to sell it to you either there and then, or at the counter) because they assume that most Americans already have some sort of rental cover built in as part of their household insurance / bank account / other financial product etc.