Spacing, lead dress, layout, etc. is the end result of a mix of many competing factors.
I
think the Weber is trying to avoid presenting the can o' worms in favor of giving a simple "rule" to follow, based on your post. I'd advise you not to take it as gospel.
Below is the preamp of my last amp build. I didn't bother with "heater phasing," didn't follow any particular spacing rule. I did consider a number of factors when deciding how to arrange the parts & wiring, including the potential for hum. This preamp (and the rest of the accompanying amp) is free of hum or noise up to max volume. Turret spacing is broadly-similar to Hoffman's spacing (3/16" to 1/4" or so, I don't really recall).
I read somewhere if the circuit wires are closer together (parallel) they cause less capacitance in the circuit than if they are farther apart which can cause more capacitance in the circuit.
Closer = More Capacitance
Types of capacitor Scroll down to "Theory of conventional construction"
If you make the 2 conductors so they have a larger surface area ("A" in the equation), capacitance increases. If you move the plates/conductors closer (by making "d," distance, in the equation smaller), capacitance increases. The other term in the equation is a value based on what material separates the 2 conductors.