The detailed is captured by the recording, so, I personally don’t believe a headphone is detailed, but rather the transducer has a certain level of clarity that allows the listener to hear the detail better. The amp and DAC can contribute to the ability to add or subtract the level of clarity, but nothing will effect it more than the headphone.
In my opinion, detail retrieval applies more to the mics and recording equipment used to capture the music and the ambience & acoustics of the recording space. I.e. are they retrieving and/or capturing everything being produced by the instruments, voices and acoustics in the recording space. A headphone’s job is to playback the signal accurately and clearly; some do a much better job than others, though.