Read your manual, it should say something like change oil every 5000 miles in normal conditions, or 3000 in severe conditions (mostly city driving, short distance, go and stop, towing, hot ambiance, etc).
What CarX told you is a conservative interval. They are using dino oil. But for dealer, are they using syn oil on your car? I doubt it. If they did, they would have told you to change oil at 10000mi or 7500mi. You can call your dealer to ask what kind of oil they put into your car.
For most people, going to dealers for oil change is close to, if not completely, throwing money to the air. But, if that is the way to make people sleep better at night, go for it. Otherwise, sleeping pills cost money too...