If all your interested in is the positive differentiated signals, no need in having a long time constant with the negative signals, just make them happen fast and forget about it.
And in the example in AoE, all they were interested in was the positive pulses. They said it, in the very first line, There are occasions when you use a diode to make a wave form of one polarity only. and specifically in the third sentenance, For instance, you might want a train of pulses corresponding to the rising edge of a square wave.
There have been many times, in timing circuits where one would square the oscillators sine wave and then develop triggers on either the leading edge or trailing edge of that square wave.
