Note that by "perfect" I mean that the level of distortion is well below
(at
least one order of magnitude) what's considered audible.

Well, that's quite a different thing. We know for a fact that all
amplifiers produce signals that distort the original.

Of course. As you pointed out earlier, simple copper wires distort the
original too. But, in the context of this conversation (which revolves
around audibility), they can be considered perfect.

Claiming that these
distortions can be measured would be akin to claiming that you can count the
number of molecules in a glass of water, which is silly.

You CAN count the number of molecules in water. You measure the amount of
water you have and you divide by the molecular weight at that temperature.
If we've only got a few molecules of water, we can't make this
measurement. But then again, there are so few that it wouldn't make any
sense to drink it. Similarly, if we have enough distortion we can measure
it. If the distortion is so small that it escapes measure, then it
doesn't matter to us anyway because we can't hear it. Again, you're
having trouble understanding that TEST EQUIPMENT IS MORE PRECISE THAN THE
AUDITORY SYSTEM. This is in all the textbooks. Want references?

Yet according to
you, these devices measure with complete precision. The bottom line is that
you're just guessing as to the accuracy of test equipment vs. the human ear,
simply because you haven't heard otherwise.

No, I'm not. The accuracy of test equipment is in the manual or on the
back of the instrument itself. It's also plain as day when you use the
subtraction method that I mentioned previously. As for the human auditory
system, I've outlined its shortcomings as best as I can without getting
too technical. If you prefer, I can get as detailed and technical as
you'd like. After all, it is my field.