Here's a pic of the Coleman grill that came with my 390. It is definitely "factory" as the pull out rails have a bracket that fits the legs of the grill to keep it in place.
The issue with using the quick connect and an adapter for the grill's regulator is the trailer supply at the quick connect is regulated (low pressure) and the valve with the grill is for a high pressure 1 lb bottle.
I haven't found anything that will let me use the quick connect and screw it directly to the grill. The quick connect extension hose I have has a ball cock valve on the end. That will act like a valve, but I haven't found an adapt that will screw into the grill.