Your are all correct!
People make the the assumption that the FAA regulations are BLACK and WHITE, they are not.
A 121 carrier is required to develop a series of manuals that dictate what the procedures are for dealing with common issues and how they comply with the regulations.
The FAA approves that manual through the CMO assigned to that airline. That manual provides a framework of how the airline complies with the regulations.
It is quite possible that Airline A's CMO may approve a manual saying up to 19 passengers may be carried on a 148 seat MD 80 with no FA's
It is quite possible that Airline B's CMO may require that all seats above 19 must be MEL'd before up to 19 passengers may be carried on a 148 seat MD 80 with no FA's
Airlines C, CMO may say no how, no way, you can never carry passengers without an FA.
For the point of this example it does not matter if the passengers are company personel, non-revs or paying passengers. What does matter, is the approved procedure in your company manual.
For many regualtions, the differences in approved procedures from one airline to another can be eye-opening.
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