Let me try to explain it this way, through a test you can do yourself, with your own dog: Leave the dog confined in a crate, in the house… and go in the yard, and collect some of your dog’s feces. Now, spread out some plastic trash bags around the living room, and place the feces on the plastic trash bags (not in the bags… on the bags, out).
Next, put the dog in the room, and immediately leave. And when you come back in the house, I can guarantee you that the dog will show you the same submissive “I’m sorry, I’ve done something bad” body language she normally does, EVEN THOUGH YOU LEFT THE FECES THERE, NOT HER!
So, yes… the dog has formed an association. Could it also be that you’re leaving her too long? (I can’t remember your original post.) Giving her too much freedom (dog should be in the crate)… or that you’ve caught her in the act before and corrected her, but the correction wasn’t quite motivatoinal enough to get her to stop.
You can get her to use the dog door by playing ball or fetch through the dog door. But she’s still not going to have any reason to use it if she knows she can defecate in your house and not immediately associate a negative with that behavior.
-Adam