My understanding is that the excess is not the full extent of your liability in the USA, as we understand it to be in the UK.
In the event of damage, if they believe that you are in any way at fault, the owner's insurance company will sue you for their costs.
From confirmatory discussions I have had in the USA with local renting pilots, I would not rent an aircraft in the USA without renters insurance, whether it was specifically required by the owner/FBO or not.