There is one mechanism related to how we perceive loudness at low frequencies, where lower frequencies need to be louder than mid frequencies to sound the same loudness. This means the distortion overtones at higher frequency than the LF fundamental note are easier to hear.
Another perceptual clue, which may not be the dominant one for woofers, in nature when we make louder sounds they are more complex (more distortion overtones). A singer at low level can make almost pure notes, while that same singer singing louder will make more complex sounds, with more overtones present. From experience we associate distorted with loud, because it usually is.
Finally an observation... Woofers have been making so much distortion for so long, that many system operators have become accustomed to that as their normal baseline. The distortion in woofers is not as nasty sounding as distortion in other frequency ranges, and actually supports the lower notes that may not be reproduced very strongly. Many in the audience hear the distortion and just consider that part of the original sound. Sometimes even thinking the speaker has response lower than it really does, because of the distortion that is present.
This must be extremely annoying to a company like Danley, that makes low distortion woofers since operators accustomed to the previous high distortion "normal" may now think something is missing.
The customer is always right, even when wrong. Note: they do make add-on effects units that introduce LF distortion (to make speakers sound like they go lower), so you can make Danley speakers sound like other speakers by adding distortion ( but why?).
System operators need to be aware that all that old school distortion is not part of the original signal, and learn a new normal. While I can imagine a scenario where a club meeds to keep SPL down, so faux bass is better than real bass, kind of like the loudness knob on your hifi receiver.
[edit] OK, not exactly, loudness is an EQ contour not added distortion, but more perceptual trickery to compensate for Fletcher-Munson constant loudness curves. [/edit]
JR