You're leaving is hanging on some of these questions but I'm thinking they salvage a radio from the car you rented that one weekend that you paired to and returned without removing your device.
I kid of course, but the real questions are.
Does the car show up in your paired devices now?
Does your phone show up in the cars paired devices now?
Is the Ruters news sometime that you ordinarily listen to?
Why do you believe that car paired to your device and that the news thing wasn't just XFM or something part of the radio features? How do you know it was your phone?
Could it have been a prank? Family member playing with you, setting sometime up.
I posed this to Google in several different ways and the best logical answer I got was a hardware glitch, which still doesn't make sense. I will say that a couple of years ago when I started noticing all these AI ordering boards at restaurants that they were eventually going to make it so that when pulled into the drive thru the car radio or your phone would automatically connect to each other to allow you to order without waiting to get to the speaker. Then sometime pointed out the pairing issue involved but I pushed back that they'd find a way. Now you're the beta tester.
Give us some answers, we're curious.