as O'Brien actually places Troi in command over various other commissioned officers in the scene, by being very quick to point out that Troi has the most pips in her collar. This despite other officers clearly being more experienced and more likely to actually be in the formal chain of command - chiefly, Ro Laren, whom O'Brien sees as trouble.
Clearly, the word of the Chief carries a lot of weight, even in officer-to-officer pissing contests.
In most military commands, the chain of command IS that Troi, by virtue of being of higher rank, is in charge. The captain, the XO, and the 2nd officer (data) where not on the bridge, And Troi outranked Ro by a fair margin (2-3 full ranks) Troi was Lt. Commander, and Ro was a ensign or a Lt (Junior Grade) at the time. (Been a while since I seen the episode, so I would have to count pips) There is no way a Lt. commander is going to be ordered by a ensign, but Troi shows good leadership skills and listens to her Non-commissioned officer and leads. (As leading many times is listening and giving orders for others to do)
Ro does not buy into the chain of command, and wants to do what she thinks is best, and also follow the NCO, but she a rebel.
As for the Senior NCO like the Chief, they do carry a large amount of weight,