There is an approach to developing a performance that substantially borrows the gestures, pacing, emotional shape and styling of another musician's performance of the same piece. This approach is often referred to dismissively as 'copycat' performances, or 'other people's music'. The critics' view is that people should develop their own interpretations, make the music their own, and that copycat performances are derivative and thus artistically empty.
Now, I am not going to argue against these critics. I have also been brought up in artistic traditions that value an individual's own take on a piece, that regards the point of performance as to give a view of some music that nobody else could give. But still, the people doing this aren't going out of their way to generate empty, clichéd performances. They experience them as real, as heartfelt. So I thought it worth stopping to investigate in a bit more depth what's going on here.