Many of the pilots may have come from the military, but Delta is not the military. Absolute respect for "the hierarchy" is asinine..
CRM on military jets, at least within the US Air Force (I can't speak for other branches or nations), is in-line with what you'd see on a commercial jet among western airlines with modern CRM practices and rank (hierarchy) is not the be-all-end-all.
If there was indeed a real emergency, the Captain should have informed the crew before he, himself, walked off the plane.
Emergency or not, the Captain was wrong.
Except, there wasn't a "real emergency". The plane was parked at the gate, with the door open and the jetway still attached. For all you know, the Captain was going up the jetway to talk to the GA about the decision, probably a reasonable action in this circumstance.