Perhaps the one lasting effect of the timeline changes that occurred in Yesterday's Enterprise
was that O'Brien never went to the Academy...
I'll go with that. Some time stream alteration changed O'Brien's past. That's more plausible than a well-established organization like Starfleet having inconsistent rank markings. I'm not being sarcastic, as far as Star Trek goes that is the more plausible reason.
Q might have had something to do with it, as well. Remember his DS9 remark to O'Brien?
"Weren't you one of the little people?"
Q altered time to stick it to O'Brien. In fact, he had such little use for O'Brien that he didn't put him on mock trial in Encounter at Farpoint