Star Trek has always been pretty shaky with issues of rank. I’ve just come to assume that, in general, Starfleet is rather informal with rank, as well as giving lots of latitude to commanding officers. So if the Captain wants to make an enlisted man a department/division head, then he’s free to do so – just like a Captain can make a skinny 15 year old an ‘Acting Ensign’ if he wants.
It’s even worse in the JJ Abrams Star Trek (which I enjoyed, despite the many flaws) – Kirk somehow goes straight from the Academy to First Officer of the flagship (!!), a position which in the US Navy today would require close to 20 years of service, and shortly after, to Commanding Officer!
As for O’Brien, he’s clearly qualified for any position up to and including Chief Engineer of a starship or space station, so I don’t really have much of a problem with Picard/Sisko/Starfleet giving him more responsibility and authority than a CPO or even Senior Chief would have in the US Navy.