It depends on the nature of the peaks. Some short-term peaks are too short to be perceived as "loud".
If you make an MP3 or a vinyl record, usually some peaks are made higher and some lower. The new-highest peaks make a 'better" crest factor without changing the sound of the dynamics. (But that's usually just a couple of dB.)
There is
software for doing your own
Blind BX Test. ABX testing of hardware isn't easy but when you are comparing audio files, the software can do the blind switching and randomization for you, and it only takes one person and a computer.
P.S.
I agree with the author's premise, but he says a couple of things that aren't true:
Techtronix started selling oscilloscopes in the 1940s, and it was invented before that. And you could build a peak detector with vacuum tunes. (I've built several peak detectors with op-amps.) And it's super-easy with digital files... You just search-through the file for the highest positive or negative sample value.
Tube amps can have headroom for peaks. They only "peak round" (AKA "soft clip") when overdriven. And although tube amps
tend to soft-clip, the actual performance depends on the design. Guitar amps (both solid state and tube) are designed to "soft clip" for "pleasant distortion" when overdriven.