No, I don't have an answer to the problem. As any IT support person can tell you, printer problems are notoriously difficult to diagnose, particularly at a distance.
I have used USB printers, and wirelessly connected printers, with OS X for years (both with built in networking and via external print servers), none of which were on the AIRPRINT list. I've also managed Mac using printers shared by Windows Server. All of these work just fine as long as there are OS X drivers for the printer (which covers most printers nowadays).
A company as successful as Apple would never impose the limits that you posit on their flagship OS.