Have just bought 2007 300c and drove from south coast to north east England (220 mile) and the main thought on the way home was "Find a Chrysler forum", so popped it straight into my browser and here I am the owldest fart with a lookalike Bentley.
Yes I can confirm you are definitely barking mad.... On another note and in answer to your question it should lock when you lock the car. I've just checked mine and it's locked, although annoyingly it does stick out a little and doesn't sit flush with the bodywork.