No not necessarily. Symptoms of a faulty door latch can manifest themselves in very strange ways. We just replaced a door latch in a 2004 Allroad because the poor guy kept having his keys locked in the car, with the key in the ignition. The car thought the key was out of the car and that the lock should be engaged so it locked itself, even though he did not try to lock it at all...the poor guy thought his car was possessed.

Another symptom is if the alarm goes off when trying to start the car, along with the symptom you are experiencing. The door ajar warning is just yet another symptom but you can have all or only 1 of these symptoms with a faulty door latch. Tricky little devils they are...