I don't know whether I can shed light or confusion on the one topic.
First I'll go to the barbershop quartet, and its quest for the "5th note" which can only be achieved through precise tuning of all four voices to produce the phantom 5th note above. Barbershop quartets sing a capella, with no accompanying instrument, esp. piano, because of the effects they want to produce.
Likewise, a string quartet wants to create effects. You can have a major chord that is brighter or less bright or disturbingly bright, all of it as part of musical expression. So in the original example, the string player with perfect pitch who couldn't adjust would destroy the sought after effect.
You can't compare that to "what if there's a piano" because those won't be the same musical goals. Or there would be a compromise of sorts.