Not directly related to the presence or absence of AM in modern car radios, but a colleague of mine mentioned that in his wife's car (don't know what make) if you shut off the car, the radio will record whatever station you're listening to, and when you restart will pick up playback where you left off. He gave me the impression that there was only a certain length of time where the recording was saved. I'd guess that it's aimed at those listening to long form programming (special features, talk shows, etc.) you won't miss anything. Kind of weird in that you may not be listening in real time.
From what he says, the feature can be turned off, but I got the impression it was enabled by default.
Anyone have any experience with this?