What book is that? I'm curious, because my experience does not match what you are saying.

Propeller performance is affected by way too many factors to make a blanket statement that two sizes of prop are the same. Airframe and engine design are just two of the big factors.

Not only that, but the same size prop in two different brands will often perform very differently in the air.

There might be some engines and airframes out there where those two size props handle the same in the air. But I am sure there are airframes and engines where there is a noticeable difference as well. A high-drag trainer such as the Nextstar is going to show less effect from changing props than a cleaner design. A clean high-speed plane, or an acrobatic plane will show much more of a difference.

Different engines in the same size also seem to prefer differnet size props. The porting and timing of the engine does matter, though most sport engines are pretty close to each other. Engine performance is not linear, so differnet engines produce their peak useable power at different RPMs and with differnet props.

For example, the OS LA series of engines generally to like to spin bigger props at lower RPMs. If you put a smaller prop on them, they don't turn up the revs other engines might, but when you put an over-sized prop on they work better. Other engines I've run really don't like turning the big props, but come alive when lightly loaded with a small prop that allows them to really crank up the RPMs.