It's all a matter of perception, a certain kind of perception, one that doesn't include the 'me' part, a voluntary parting of the ways between the self that is me and the self that is doing the thing. Bill Morgan calls it an 'enculturalization", a key and formative part of any training, a part that is more myth than physical musculature reality:

No matter how high you jump, how fast you run or swim, how powerfully you row, you can do better. But sometimes your mind gets in the way. "All maximum performances are actually pseudo-maximum performances ... You are always capable of doing more than you are doing".

[cyclist Gina] Kolata recounts how this applies even to the everyday struggles of training: "I concentrated on my cadence, counting pedal strokes, thinking of nothing else. It worked. Now I know why. Dr. Morgan, who has worked with hundreds of subelite marathon runners, said every one had a dissociation strategy."
[ I'm Not Really Running ]

In the 'Zone'

I've had that sense too, not in an endurance test, but in the making of sound, in that moment when your body+instrument meta is able to create something that truly leaves the 'you' standing in the shadows like a fool. Which is not to say that this is the whole of the story because musicians also know of an additional twist (which the atheletes may recognize if they were asked) where the 'me' who is doing the playing is actively and deeply engaged, but the 'me' who would criticise and correct and instruct the playing is the sidelined wallflower. Not surprisingly, as is the new stock paradigm of neuroscience, when we have an observation about our self-experience, we find it mirrored in the brain-scan:

when jazz musicians are engaged in the highly creative and spontaneous activity known as improvisation, a large region of the brain involved in monitoring one's performance is shut down, while a small region involved in organizing self-initiated thoughts and behaviors is highly activated. The researchers propose that this and several related patterns are likely to be key indicators of a brain that is engaged in highly creative thought.
[ Prefrontal Region 'Takes 5' To Let Creativity Flow In Jazz Improvisation ]