Airplane controls are somewhat of a hybrid between regular controls and inverted controls. Since you do indeed input up to look down and vice versa, but you still input left to turn left and right to turn right.

Isn’t that how inverted joystick controls in modern video games work too? It’s only the Y axis that’s inverted, I thought (and only the “viewing angle” joystick, not the “player movement” joystick).

Airplane stick is actually consistent but in a different way. The stick always rotates the plane around it's center in the direction the stick is moved.

It's an example of "move the object" instead of "move the observer", in that the goal is to control a vehicle not to control the view in the windshield. And the "object" you're "grabbing" is only rotating the vehicle around it's center, not panning around a flat surface.

Fully inverted: ‘Like an airplane for up/down, like a yacht for left/right’