I wouldn't be satisfied with that response and I'd pursue it up the corporate ladder. I don't believe that's a reason for them to kick you back to the local branch. Keep calling CS until you get the right answer. As you seem to recognize, there is a potential here for a big problem. Do you have a boarding pass or other proof that you flew that day?

Mistakes do happen, so I wouldn't jump to the assumption that the check in person is using the car in a crime wave. But this is not something to let go and you need to stay on top of it. Make sure you're documenting who you spoke with and when.