We're in big trouble if we can't agree on a definition of accuracy.
It's true that the most appropriate goal for live music reproduction is the creation of an euphonically pleasing recording, in part because that is a goal which is actually achievable. An truly accurate reproduction of the live event is simply and demonstrably not possible. We know that because we can define such accuracy in specific, objective terms (upon which one quickly realizes that achieving it outright is impossible by all practical measures), whereas we cannot fully and objectively define what makes for a euphonically pleasing, emotionally convening audio playback experience. Instead we "know it when we hear it" and become willing participants in deceiving ourselves that it sounds "just like it did live", when by truly objective measures of accuracy it both does not and cannot. Yet in the end that short coming is inconsequential. All that maters is that the listener enjoy the result to the fullest extent possible, that they can easily, willingly, and unconsciously suspend disbelief so as to experience playback as if the live experience is actually being recreated in a way that feels accurate to them in a totally convincing way.
How to get to that appropriate subjective goal is the more useful and pragmatic question. There is more than one road to Rome. Some do it by developing a method and signal chain which produces a recording which maximized those qualities without further manipulation, or with minimal further manipulation. If one part of the signal chain is less than accurate in one way, introducing something else in the chain which is less than accurate but in an inverse way to the other part does reduce the inaccuracy. In this case, a wrong + an inverse wrong = something closer to right. Some do it by striving for increased accuracy over euphony throughout the capture phase to the extent that such is practically achievable, with the intent of making the most effective appropriate euphonious manipulations afterwards.
Neither method is correct nor incorrect. That mastering engineers are valued for things other than simply converting and packaging content for release (and that great ones are well compensated for their ability to make subjective euphonious manipulations) is acknowledgement of such. Those guys both know and trust objective specifications, and also know and trust their subjective intuitions. They know how to handle both and are more aware of the appropriate intersection of those realms than most.
This is similar to alternate uses of the word truth. Sometimes that world is used to refer to factual truth (objective "agreed upon" truths), sometimes emotional/poetic truths ("it's true to me"). Conveying meaning accurately depends on agreement on the definition of the terms used, by both the speaker and audience. Funny ha ha or funny weird?
What we have here is a failure to communicate. What we have here is, on the face of things, an argument about method (which road to Rome), with and a deeper disconnect concerning agreement of which Rome we're referring to - for some it might be one of the 21 different communities named Rome in the USA, for others its the big one in Italy.