Something along those lines is done in some places, but it is not foolproof. In the current case, the four could have driven there in one vehicle and left one cave card on the dash.Another option is the state specifying that "you must have one of this list of cave certifications from one of these recognized organizations to dive here or we will arrest you for trespassing. Please leave your cave card and gate receipt on you dashboard when you go diving."
A couple years ago I was diving at Gran Cenote, and we did not realize we would have to show our certifications to get in. Fortunately, Lynne Flaherty had brought all her various level cards with her, so both of us who did not have cards with us had something to show. The guy checking obviously did not notice or care that 3 people had the same name, and that I, obviously a male, was named Lynne.