While specifications are normally based on measurements, they don't show much of the whole picture and can also hide much. Distortion will vary with frequency and power. In order to see the whole picture and really know the distortion characteristics of an amplifier, complete measuement graphs needs to looked at. This is well known among those who understand measurements.
For example doesn't rated power tell us much unless we know the distortion level with that power. Power can be listed with a numerous distortion numbers. Typically used 1% THD is actually very high audible distortion and is far from decent hifi. We don't have strict guidelines of how distortion should be listed. One manufacturer might list the wattage to be with aTHD distortion of 0.1%, another 1% and another 0.01, etc. It's impossible to know unless graphs are actually posted. And seeing how the amplifier rises in distortion with power, it's important.
When someone speaks about the importance of distortion levels in regards to the audible quality and mentions weaknesses in how other amplifier measures in this regards, but fail to show any graphs of their product I personally get very skeptical. Why not post graphs to back up the claims?