It seems as if having such a standard of impeccable identity with the original only keeps one from being happy with an excellent instrument.
Only if the instrument doesn't match their expectations, and of course expectations vary. For me, I'm normally not too picky about things like exact knob/slider positions, because these are the types of things that could vary quite a bit from unit to unit due to manufacturing variance. Sometimes you need to nudge a knob an extra half millimeter on one synth to achieve the same sound on another of the same model. But, if the two sound no where near each other within like 25% of the total range of the knob, that would be a problem. Or if some basic fundamentals like the saw waves, noise type, filter etc just sound nothing alike then to me that's a bigger problem (for my own personal expectations) because if the fundamentals aren't there, it means it's only a "loosely inspired by" synth, which is of way less value to me than a proper reissue.
But, I do agree, at some point a synth either captures what an individual ear liked about the original synth its based on, or it doesn't. And if it does scratch all the right itches, then it probably should be obtained... as long as that criteria is satisfied, it really doesn't matter at the end of the day if sound matches identically or not.