If the cops had probable cause, then she is required to identify herself verbally, she does not have to "show papers", but she must be truthful.
If the cops have probable cause to believe that she is untruthful or is involved in the commission of a crime, they may hold her for a reasonable number of hours (determined by local courts) to ascertain her identity.
Assuming that she was with her husband and that he identified himself verbally, I think the taxpayers are gonna take it in the shorts this time.
I am guessing probable cause. They got a report of lewd behavior. She and her boyfriend were having sex IN the passenger seat WITH door open and cleaned up afterwards with tissue according to witnesses. No decent woman does that in broad daylight.