IMHO there is one very important variable that is missing from such claims. You cannot "hear" the amplifier directly but instead must use a transducer of some type to do that, e.g. a loudspeaker. Loudspeakers and more specifically their drivers have a wide range of sensitivities, from 80dB/W to 110dB/W. Noise is much less of a concern when you have a low sensitivity loudspeaker like a small 2-way or whatever. On the other hand a DIY speaker using a compression driver and horn with an active crossover has the amplifier directly connected to a very high sensitivity tranducer, and in this case even small amounts of noise/hiss in the amplifier can be audible in the absence of a music signal. So for noise, what you will be using for a loudspeaker definitely has some bearing on the level that is acceptable.
As far as distortion goes, for harmonic distortion the order matters as well as its level. This is because masking is weaker for higher order distortion and the fact that humans actually "like" some low order (primarily second order) distortion to the point that some actually try to use equipment (amplifiers and preamps) that impart this sort of harmonic signature, sometimes called "euphonic distortion". But above 3rd order you want distortion products to be low. Unlike noise, these are only present when there is a music signal and so it is a matter of how anal retentive you want to be with respect to "signal purity" and how much distortion you think you can perceive. There are probably online tests for this, and each one of us probably has a different sensitivity to higher order harmonic distortion. Finally there is intermodular distortion. This is when two or more tones occuring at the same time give rise to other tones that are sums and differences of the original tones AND the new tones as well. The new tones are not harmonically related, so what you get is a mess that is not quite noise but would probably cause a loss of fidelity and clean-ness of the signal once it gets bad enough. Also, keep in mind that the frequency of the distortion product is important. 3rd order distortion produced by a 5kHz fundamental tone is not really going to be a problem because it is on the very edge of your hearing, or possibly above it if you are a bit older. So when an amplifier has a bit of a rising distortion signature at e.g. 5-10kHz that is no concern for me.
Of the distortions I mention above, the loudspeaker produces much more of them compared to DACs or amplifiers that are manufactured today. Even a cheap $150 class-D stereo amplifier likely has a much cleaner transfer function than the loudspeaker! So keep that in mind when you are scrutinizing amplifiers using these metrics.
And to put things into perspective WRT human hearing, a very quiet room is around 40dB and a very, very loud sound might be 110dB. That is so loud that exposure for more than a couple of minutes can give you some hearing damage like tinnitus. This is a range of around 70dB, from the loudest sound to the quietest roughly speaking. So when your amplifier has 90dB SINAD you are already getting into very decent performance. Since SINAD is a composite metric of noise and distortion you need to look a little deeper into their contributions. I would take a low noise but higher distortion amplifier over the opposite, for example.
