Why is the center of pressure of a rocket at its centroid?
This answer may not be what you are looking for, but I think the issue is we aren't really talking about the rocket as a "wing" here since these rockets fly ballistically.   I think the term CP in the NASA article would be better expressed as "neutral point", the point at which aerodynamic moments are in balance when the rocket is not aligned with the airflow, taking into account the body and all of its appendages.  

So this would include the fins as part of the total lateral area subject to lateral air loads when the rocket yaws while flying ballistically, and to be stable, the rocket's center of mass needs to be forward of the neutral point, so that when it yaws, the corrective moment, acting at the aerodynamic neutral point, is created about the center of mass to bring it back into alignment with the airflow.

The term CP suggests that the rocket is flying like a lifting body wing, with a constant angle of attack and lift being generated to support its weight.  But as a ballistic object, its AOA is always ideally 0 and what lateral aerodynamic forces are being created are strictly to keep the rocket's tail lined up behind its nose as it travels its ballistic path.