A few inaccuracies there:
- If somebody's rank is "Chief Petty Officer", this leaves open three or four possibilities, as the rank in real life comes in three grades (CPO, Senior CPO, Master CPO) plus the honorary rank of Master CPO of the Navy (a single individual who's chosen to symbolically represent the entire enlisted force of the service). So even though the mention of O'Brien being a "Senior" (from "Playing God") precedes the Jem'Hadar assessment of him being a "Chief Petty Officer", we don't have to believe the Jem'Hadar were wrong or O'Brien got a demotion.
- The use of words "rank", "rating", "grade" or "position" is complex in the real world, but Trek seems to make it even more complex. In "Tribunal", O'Brien clearly states that Chief of Operations is his rank
, not (merely) his position. We just have to swallow this with a grain of chloride of our liking. (Perhaps O'Brien was just saying that his rank was Chief, and then clarified it with his specialty being Ops, and all the torture made us miss the comma in between?)
- O'Brien was never really referred to as Lieutenant anywhere in TNG. Rather, the word "Lieutenant" was once uttered in his presence in an ambiguous manner ("Where Silence Has Lease"), and might just as well have been directed at Lieutenant Worf. In contrast, O'Brien was once clearly claimed to be a Chief Petty Officer ("Family") at his face, a claim not challenged on the spot, and never truly contradicted later, either. It was just his collar markings that varied wildly.