For a simple example, any music that “grooves” (makes you want to tap your feet) tends to not be perfectly sub-divided into 4 beats. Different players in the same band may be intentionally (and/or subconsciously) hitting their notes on different parts of the beat to increase this effect. In this type of scenario there really isn’t any substitution for practice and “feel”, a metronome would never get you there.
In terms of piano, GP may have been referring to rubato, or holding notes for longer/shorter than notated for artistic effect.
Agree, "perfect accuracy" was a bad choice of words. When learning a new song it's best to "never play a wrong note" – to make sure you play each note with 100% accuracy, no matter how long it takes you. This trains your muscle memory much more efficiently than playing less than perfect and undoing the muscle-memory-learned mistakes as you go along.
Pop and jazz have "the pocket", which is where the groove clicks into maximum effectiveness.
Classical has phrasing.
IMO it's the same phenomenon. It's one of the most effective ways to add expression, and it's mostly taught aurally. There's very little in books for beginners about it.
If you're taught to play metronomically, you may never understand why it matters. Someone who is naturally musical will feel it without being told about it, but may still struggle to bring it out of their playing.
In terms of piano, GP may have been referring to rubato, or holding notes for longer/shorter than notated for artistic effect.