I find that far from obvious. To me it would make more sense that she would be able to park there while she was transacting business inside.
You act like everyone who rents a car must leave their car at the rental location. That's ridiculous. Where were you in all of this? Wouldn't it have made more sense for you to drop your wife off? Or at the very least drive her back to pick up the car and leave it at your residence?
Okay. I don't wish to be rude, but that is just stupid. I have stated repeatedly that they gave her permission to park the car there while she was a customer and driving the Enterprise car. You think that them giving her permission to park there means they were giving her permission to park there for five to ten minutes while she was inside? "Just so you know, ma'am, we give you permission to park in our parking lot for the next five minutes." You actually think it would make sense for them to give her a sign to put in her windshield identifying her car as that of an Enterprise customer only for while she was inside the building for five to ten minutes? What other businesses give you a sign to put in your windshield so your car doesn't get towed while you are inside the business for ten minutes? If you go to a Walmart parking lot would you expect all the cars to have "Walmart Customer" signs in their windshields? I'm sorry, but that is just stupid.
And, no, you don't have to leave a car to take a car at a car rental place. Nobody suggested that, and that has nothing to do with the question at hand. The point is they told her that her car was authorized to be parked there, and they were, evidently, lying.