In the middle of the night, not in a neighborhood, not outdoors, but in a private car, two adults have consentual sex. What's the crime here? There's absolutely no problem with a group of policemen finding a car on the side of the road at night suspicious. They are doing their job. But to arrest these individuals is unreasonable. A simple warning and asking them to leave would have sufficed. That the news breaks out and people get interested since two public figures are involved is also normal.
It might be a crime in US to have sex in a private car. But USA is a country of puritans. But trust me, in Europe, it is not a crime. You are just asked to carry the activity at your house. You don't spend a night at a police station, justifying to the poice why you did what you did.
But I am sure it is a crime in ismalic countries; you may even get your head :) chopped off.