Let's have some fun...
I haven't thought this all the way through so I may change my consideration, but, for the moment, I'm very leery of this question being useful. We see the question (posed rhetorically) a lot, often mid-squabble. It's kinda an expression of sheer scepticism that can be used to thwart any attempt to come to a conclusion. We also see it associated to a list (Ron's ?) of 4 Types of Audiophiles, one being those who seek reproduction true to what is on the recording, or some such.
Microstrip's formulation (above) taken from Dave C's cue asks about the artists' intent. This is somewhat problematic because intent is difficult to gauge through listening. If they're still around, we could ask performers - "does this recording exhibit what you intended?" Suppose they say 'yes' or 'no' - what does that tell us? That the recording is faithful to their idea of what they wanted it be? Huh? What does that tell us?
Inspired by remembering that Descarte's scepticism ("How do I know that I exist?) was ultimately the cause of his certainty (cogito ergo sum), I'll rashly answer the question. :-O
We start with the notion that at such-and-such a time and place the XYZ Orchestra of the Air along with The 4th Street Belmont Singers performed Brahm's Schicksalslied Op.54 and that was captured by microphones, etc. and put on tape.
There was an act of recording; the verb. But is that 'the recording' ? If it is, all the scepticism boils down to saying we cannot relive the past, so we can't really know. Even if we could, that's not the recording of a performance, it is the performance.
Is the so-called 'master tape' the recording? No, it's a magnetic tape on a metal reel. Even if you hold it close to your ear you won't hear the Song of Destiny. Not even a pre-echo.
I reject the notion that "the recording" exists as some kind of timeless objective Platonic Form that is The True Recording, that it is something we can never truly know, something that at best we can only grasp as 'shadows' of the recording. This seems to be the angle where the question is coming from.
Music is performance art. It exists in time and is transient. A recording must be performed to hear music. It moves from the potential (media) to the actual through time - when the recording is performed, when the record is played. Every time you play a record you hear exactly what is on the recording.
We can't and we never will. And the reason is pretty fundamental. Even if all our playback hardware was designed to perfection, every last playback system would still fall way short of sounding EXACTLY like what's on the recording. For the simple reason that every last component, speaker, line conditioner, cable, etc is incomplete in its design. This incompleteness is far and away the greatest dificiency in high-end audio.
Completing a design is entirely outside the scope of the designer but well within the scope of the consumer. Think noisy AC, unwanted mechanical energy, speaker placement, room acoustic anomalies, etc. Even the best product designers don't realize how incomplete their designs are. For example. One highly-regarded designer admitted in another forum that all his designs as well as all others' designs contained at least one serious unknown flaw and measuring instruments were of no value in this regard. I never listened to any of this designer's products but I assured him that his designs contained no such serious unknown flaws but rather they were simply incomplete.
IME, these are the primary causes:
1. Audible and inaudible distortions. (Most catastrophic distortions)
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We know for a fact that any given recording, good, bad, or ugly contains exactly 100% of all the music we hope to hear via our playback systems. With digital we know the exact size of a given recording down to the bit.
System-induced distortions have numerous sources but the most catastrophic distortions are induced the moment we power up our playback systems while some others are induced the moment we push play. Regardless, all distortions combined determine a given playback system's noise floor. The noise floor is key it determines the percent of music info at the speaker that remains audible above the noise floor and inaudible below the noise floor.
IOW, it's a percentage thing. If (and it is so) all recordings contains exactly 100% percent of the music info we can potentially hear, then these audible and inaudible distortions will reduce the amount of music info remaining audible at the speaker to say 50 or 70% depending on the playback system. That implies 30 - 50% of all the music in a given recording remains inaudible. For those who think a higher rez format containing 3 or 4 times the quantity of music info embedded in its Redbook counterpart changes things, you're wrong. 60% of a single music note remaining audible remains at 60% of a single music note. Especially since a given format does nothing to address these distortions, it can do nothing to change these percentages. Except that the 60% of a single hi-rez music note remaining audible may be now be just a tad more musical. But it's still 60%.
Secondarily, we need to consider system-induced distortions not only make a large percentage of music inaudible below a much raised noise floor but they also may corrupt the fidelity of the portion of music that remains audible above the noise floor. Additionally, when distortions cause a large percentage of music info inaudible at the speaker may also may cause the audible musical to seem distorted when it is not.
If you've ever wondered why so many playback systems have that "hi-fi" signature sound, unaddressed system-induced distortions is why. This also explains why the early out-of-this world MQA performance claims were entirely untrue. This is also why a closely-mic'ed sharp piano strike in the upper registers can cause ear fatigue. This is also why so many of us have trained ourselves to listen at lower than live music volume levels. This is why some unsuccessfully opt for multi-channel. I could go on with many more examples. as system-induced distortions and the resulting noise floor and percentages of audible vs inaudible music info at the speaker will sufficiently explain maybe 80-90% all all deficiencies within high-end audio.
2. Inaudible Music Information Leaves Audible Music Info Sounding Distorted (shortcomings).
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For example. There is no substitution for THE optimal full-range speaker / subwoofer placement and tuning within a given room when it comes to truly musical bass reproduction. When we fall short of optimal speaker positioning / tuning a subwoofer, in either case a good percentage of bass info remains inaudible while much of the audible bass remains underemphasized, ill-defined, lack-luster, etc. When this happens, the overall music presentation becomes rather unbalanced hence, the presentation can seem overly bright, etchy, or even borderline ear bleeding fatiguing. But if corrected, the bass becomes vibrant, dynamic, deep, tight, fast, well-defined, and ultimately extremely musical. IOW, it becomes the foundation of the performance and often times the most exhilarating part of the entire playback presentation. And it just so happens that the overly bright, etchy, fatiguing and almost distorted miss and highs disappears at least with some systems.
In summary, a single playback system alteration adjusts the noise floor up or down a few percentage points and likewise the amount of audible vs inaudible music info at the speaker resulting in a more or less musical presentation. IOW, it's all really just cause and effect.
Cause: System-induced distortions determine a given playback system's noise floor level.
Effect: Determines the percentage of audible vs inaudible music info remaining at the speaker.
Cause: System shortcomings render some of the music info inaudible.
Effect: Audible music info is less musical and/or seemingly distorted.
The point being, without properly identifying every last distortion and shortcoming and without applying the perfect remedy for each, there is zero hope of ever hearing EXACTLY what's on a recording. And since the hi-fi sound is so prominent, many couldn't even hope to hear anything remotely close to what's on a recording.
Anyway, though there are others, these are the primary reasons why we'll never hear EXACTLY what's on a given recording. But once we realize how catastrophic some of these distortions and shortcomings really are, we'll also realize other things like why hi-rez recordings are only marginally (think small percentage) more musical than Redbook PCM, why (much like hi-rez formats) the hardware itself actually matters far less than we thought, why room acoustic anomalies matter far less than we've been taught, along with maybe 20 or 30 other why's. Not to mention putting many a folklore to bed once and for all.
Besides, even if we had the ability to hear EXACTLY what's in a given recording, who has the ears to fully appreciate such perfection?