If you want to insist that the recording is gospel, and play it back ruler flat, no EQ, then sure, that is a measurable form of accuracy compared to the recording.
 I just don't believe that is the true input signal.
 A musician goes into a studio, lays down a track (the TRUE input signal).
[3a] The engineer applies a host of EQ, compression, etc. (based on what factors, I don't know) cuts a recording. I play it back on my headphones. What do I want to hear? I want to hear what the musician played.
 I cannot objectively know what I am hearing is accurate unless either (i) I took independent measurements in the studio to compare to, or (ii) I know the entire chain of modifications that were made in the process of mixing.
 As for what is on the recording, Jude and Jerry Harvey (and assign as much weight to this as you want, I'm not saying their word is gospel) all seem to agree that a bit of a bass hump sounds closer to being in the recording studio.
 All I can do is go to concerts. I agree with you 100% that this is a terrible reference point, but this is all I got man.
 If you want to insist that the recording is gospel, then I disagree but respect your right to an opinion.
1. Of course the recording is gospel, what else are you trying to playback? What else do you expect an audio reproduction system to reproduce if not the recording?
2. The input signal is the signal you input into the piece/s of equipment you are measuring! Are you now trying to redefine what "input signal" means because I've refuted your redefinition of "accuracy"?
3. NO! ... That's just one of many "true input signals" to the studio's DAW/multi-track recorder, it is NOT the input signal to your DAC, Amp, headphones, etc.!
3a. Again, NO! That really is NOT what you want to hear, or if it is, then you're just about the only consumer on the planet who wants to hear that! That's like going to a restaurant, ordering a piece of cake and then saying; that doesn't taste anything like a completely different cake, I want the pile of ingredients that cake was made from, not a cake! Virtually never does a musician go into a studio and lays down a track, What typically happens is that a musician goes into the studio and lays down several takes, then the next day another musician goes into the studio and lays down another bunch of takes and this continues until all the musicians are recorded. All this is then edited together and then mixed, those edits and processing done by the engineer are ENTIRELY "based on the factors" of what the artist/s and producer want the the recording to sound like! Furthermore, the artist/s typically do not want you to hear the original takes because they have usually been recorded in such a way as to facilitate the mixing process, they have not been recorded to sound real or perfect in isolation (without the rest of the mix).
4. You're still doing exactly the same thing you were before; comparing two completely different things, apples and oranges. This case is even more bizarre than the previous one because one of the things you are using for comparison you don't even know, in fact no one does! Therefore, there CANNOT be any determination of "accuracy"! Now, you seem to be agreeing with this statement but then contradict yourself by effectively saying: OK then, there is accuracy but it's subjective. I'm saying; there CANNOT be any determination of accuracy period! If you want to discuss subjective opinions about your perception of similarities or differences that's fine but that is a discussion about your perception of similarities and differences, not a discussion about accuracy.
5. I suspect you are taking that quote out of context. If you're not, then they are incompetent, because if their recordings all need a bit of "bass hump" then they should have added that bass hump to the recording during mastering, that's the whole point of the mastering process!!
6. No, the reference point for a determination of accuracy is the input signal. Your reference point can only serve as a basis for a subjective opinion of the differences between your perception of a live gig and a recording, not a reference point for accuracy.
7. The recording is your input signal, you have no other input signal. Therefore as a reference point for the determination of accuracy the recording MUST be gospel. For a subjective determination of whether you prefer the recording or the live gig, the recording might not be the gospel but that's a subjective opinion which has nothing to do with accuracy!
1. Measuring accuracy is not technically impossible, although measuring it with infinite precision is.
2. Correct but then most commercial recordings are not designed to be a perfect documentary of the sound at a single point in space, they are designed to create a perception.