There is no evidence that any schmuck can be a NCO, in fact schmuck status seems to be reserved for your basic Ensign and Lieutenant before the latest movie. As the only one of his kind we have extensive screen time with Chief O'Brian come across more like the Top Soldier, who has been more rigorously selected then the young Ensigns and Lieutenants assigned to his department on DS9
This is the interpretation I take. It seems like the vast majority of people in Starfleet are officers, with the non-comms being an exception.
My guess is that you need a decent amount of training and education to work on a Federation starship, no matter what your job is, and Starfleet would rather take care of that training itself. It also simplifies the rank structure and allows anybody on the ship the opportunity to potentially rise up to be an admiral, making it a true meritocracy. Non-comms are specialists, people who didn't go to the academy but were granted the opportunity to work in Starfleet because of their great knowledge and skill.
This allows both the inclusion of non-comms and Gene Roddenberry's early claim that everyone in TNG's Starfleet was an officier.
I agree with your interpretation.
In the future, I bet they'll probably merge the Non Com into the Officer route and make everybody an Officer in name.
Yet everybody will train in the same basic skills / technologies and learn until they are mature enough to go into the command route if that's what they choose to do.