You triggered my interest. Don Stackhouse at DJ Aerotech had an interesting summary with respect to a low inverted pass with a tractor prop setup with the airplane dragging the vertical fin on the runway.

"If the propeller disk is angled slightly upward as I just described, it will also be making some additional nose-up forces. A propeller in an angled flowfield makes sideways forces, just like a wing or tail surface. This is why forward mounted props (like most tractor propeller installations) are slightly de-stabilizing in pitch and yaw, while aft mounted props tend to help stability. You can see this on the old Northrop flying wing bombers. The original XB-35 had pusher props and no vertical fins. When they converted these to the YB-49 jet version, they had to add small vertical fins to make up for the loss of the yaw stability contribution of the props. "

"The downward moving blade in your slightly nose-up inverted pass situation sees a slightly higher airspeed and a slightly higher angle of attack than the upward moving blade, so the aerodynamic drag of the downward moving blade is slightly greater. This creates an upward force parallel to the plane of the prop disk, which tends to pull the nose up if the prop is ahead of the pitch axis (usually the C/G, or in this case the tip of the fin).This force is probably negligible in this situation (although every little bit helps!), but can sometimes be very significant. For example, on the V-22 Osprey tilt-rotor aircraft, this sideways force is supporting a large portion of the aircraft's weight while it is transitioning between helicopter and airplane mode. "

It isn't the result of the air being deflected downward as it passes. It is the result of the asymmetric loading on the propeller disk. The descending/lower blade in the pusher setup has a higher angle of attack than the upward/retreating blade which causes differential lift and drag effects and results in a force parallel to the prop disk. That transfers to the CG and results in the stability increment.

It brought back a memory of test flying a model built by a friend of mine. He had an interesting horizontal tail location and size and wanted to see if it worked. The CG was calculated by him. Right after liftoff I realized it was unstable in pitch so I pointed the nose up and wobbled to altitude to try to find some ideas before I ran out of altitude. Finally he and I decided to call it quits and try to get it on the ground. When I throttled back it suddenly stopped the pitch oscillations and although sensitive was controllable. It was the prop/power pitch stability increment - in this case it got worse with power in the tractor prop configuration.