Measuring headphone harmonic distortion accurately (stress on the 'accurately') down to 0.01% or lower across the entire audible frequency range, 20Hz to 20kHz, is not a trivial matter. Because of this, it is routinely performed poorly. Most headphone distortion measurements are of THD+N (total harmonic distortion plus noise), and the noise contribution, principally the measurement microphone's self-noise (see Microphone noise), is far from insignificant.
A classic symptom of this is plots of THD+N versus frequency, conducted at 90dB and 100dB SPL, in which the 100dB SPL curve dips below the 90dB SPL curve over some or all of the frequency range. This occurs not because the distortion at 100dB SPL is genuinely lower, of course, but because the signal-to-noise ratio in the measurement is greater, and so the noise contribution is reduced.
Here's an example from Rtings.com: https://www.rtings.com/headphones/1-4/graph#1671/4029. If a measurement is so obviously wrong as this, why publish it? (BTW, the previous Rtings example I linked here appears to have subsequently been removed!)
In addition, no headphone distortion measurement that I've ever seen takes account of the distortion of the measurement microphone itself, the assumption being, conveniently, that it is minuscule compared to that of the headphone. But is it? This is explored on the Microphone distortion page.
Does any of this matter? You might argue, with reason, that 0.01% distortion is inaudible anyway, so who cares? My answer to that is two-fold. First, there is no excuse for making poor measurements, ever. Second, THD is meaningless in respect of quantifying nonlinear distortion in a perceptually meaningful way (explained here). There are better approaches, but they involve accurate measurement of the harmonic pattern, potentially to quite low levels. So we arrive back at performing the harmonic distortion measurement properly in the first place. To achieve this requires first that the microphone self-noise is reduced as far as possible, particularly 1/f noise, and second that sufficient averaging is used to suppress the mic noise further.
This is a work in progress here, the outcome of which I'll explain in more detail when HTL begins to carry distortion measurements.