As a member myself, I look forward to the answers you receive from the club, though I have found them wishy-washy and more than a little ignorant at the upper echelons of management. They actually have signs posted at the range that only 21-year-old adults are allowed to handle handguns. I honestly question if they even know the law in this regard.
I do not agree with the NRA's (and many clubs') rules of zero-tolerance for loaded firearms in classrooms. Like all zero-tolerance policies, it is indicative of laziness, and in this case, especially, it is counter-productive when trying to teach firearms as part of our individual liberties which is the basis for why we have them available for self-defense.
While NRA-certified, I will not teach NRA classes so am fortunately not bound by their idiocy in this regard. There is no "common sense" about their rule. The instructor may be technically following NRA rules or the club's rules, but "Paul" is an asshat for the way he handled it, certainly, and especially for giving very wrong reasons and showing his own personal ignorance, arrogance, and bias against unlicensed carriage of firearms.
I will also say that when I took my highest levels of NRA Instructor certification classes, we were a classroom full of instructors, and with the training counselor's blessing, every one of us maintained a loaded sidearm throughout the course, including in the classroom. That was a nice touch. And it was done in that same training classroom at that range. We all laughed as we covered the first "rule" of the classroom.
There are at least two of us that routinely open carry while shooting trap at that club; and in the presence of the club's Chief RSO, too.