I figured she'd still have seniority over him. Plus while I don't doubt that Squall cares for his squad mates, his taciturn attitude kinda leads to poor communication/conflict resolution skills that sort of make him not the best fit as leader.
Though I suppose it could be that she spent her year after graduation as a teacher/proctor instead of actually working in the field. Sort of a "Those who can't do SeeD missions, teach SeeD missions" type deal.
Also I love that even in the midst of a civil war SeeD still finds the time and capital to cut me a paycheck.
I know what you mean, the only way she could be senior to Squall post demotion, is if she had a higher SeeD ranking. Squall is given the role of leader, her teaming up with them later doesn't change the chain of command, unless she contacted Cid and he gave the order for her to take over. I do like the little touches in Timber and Galbadia Garden, where she is still in instructor mode, asking them to quote Garden regulations so they know what to do. She seems to fit the advisory role.
Squall's leadership skills do get better, against his will I might add. It's kind of thrust upon him, and there is a reason for that. You won't find out till Disk 3 if I remember right. This game is worth a second play through, you'll pick up on things once you know the full story.
Obviously the admin staff have no time for that shit, people need to get paid lol.