Actually, it's not excellent advice. The quote you reference suggests that because the "propeller pulls the airplane through the air," then pushing or pulling the propeller by hand can't hurt it. It's a ridiculous non-sequitur comparison. An air load on the propeller acting against the chord line, vs pulling perpendicular to the chord line at a single point on the propeller have nothing in common.
Unbalancing a propeller doesn't change because it's a conventional gear airplane; in fact, conventional gear has nothing to do with propeller balance. Moving the airplane with the propeller generally won't impact balance, though it can impose stresses on the propeller, hub, and engine mounts that were not intended.
Forces acting across the prop disc while the propeller is in motion, while it's being acted upon by centripetal forces, are very different than forces applied to one or two points along the prop when it's static.
Balance is a function of weight distribution, and is adjusted by adding or removing weight from the propeller itself, or from the hub or spinner. Balancing can be done statically or dynamically. I don't believe I've ever seen a propeller unbalanced by pressing or pulling on the prop by hand, but something as simple as a missing washer on a prop spinner or dressing a nick on a prop blade will lead to a degree of prop imbalance.
Height above the ground (gear height or position based on gear configuration) doesn't impact balance; balance is a function of weight distribution throughout the spinning propeller disc. If the propeller is unbalanced, it's unbalanced whether on conventional gear ("taildragger") or tricycle gear, whether close to the ground, or high above the ground. Balance issues are typically manifest at higher RPMS, though are more pronounced in certain RPM ranges, regardless of landing gear configuration or relation to the ground.
Propellers bend. They bend in normal operation. If you've ever seen the effects by looking at the prop disc from the side during a load, you'll see it coning forward with a considerable amount of bend in some cases, and in certain RPM ranges, harmonics lead to a degree of wave in the prop blade. The impact this has on the propeller blade and the load it imposes is very, very different when the propeller is spinning, than it is when the propeller is not moving, in a static state.
A propeller can be made to be imbalanced aerodymically, or more specifically, a vibration caused, by bending one blade and not the other. This isn't actually a prop imbalance, but rather a difference in the local angle of attack of the blades, and can lead to vibration that's different in nature, and imposes different stresses, than a weight imbalance. In this case, bending of a blade or changing of it's angle of incidence at a given point will cause the propeller to experience different forces at different points in the arc, as well as on a continuing basis as it rotates, and can cause unusual and unpredictable harmonics.
I'm not aware of any towbars that attach to propellers to move aircraft. Those who would suggest that one can't hurt a propeller by pushing or pulling on it on the ground (because props move airplane in flight) miss the point entirely, and might be hard pressed to explain why we don't have devices designed to move airplanes on the ground using the propeller to push or pull. Think about it.