Here is wonderful article about a pianist's interpretation: The Way is Not the Only Way.
I remember being asked in college to identify a pianist simply by listening to a recording and thinking, how in the world can I identify a specific pianist? Doesn't all classical piano sound the same? Little did I know that each person brings a piece of themselves into each performance, regardless of how "common" his choice of repertoire.
When a listener takes the time to listen to the same piece of music played by several different artists, or invests time in listening to a whole body of work by a single artist, personalities start to emerge. This is fascinating to me. Recordings by individual classical pianists are not, to the untrained ear, easily identifiable. Does this relegate classical music enjoyment to the elitist or the academic? Are artist interpretations of classical music too nuanced to be enjoyed by the average listener? Pop music is so much more accessible, right?
But think about it : a pop singer, to an "untrained ear" is also not easily identifiable. Songs performed by Michael Jackson or the Beatles or Justin Bieber or Adele might be immediately recognized by some, but to someone unfamiliar with their "sound," perhaps a child or a music-lover who dislikes pop music (!), or even your average Joe encountering an artist for the first time, their music is as strange as pianist Glenn Gould's recording of Bach's Goldberg Variations. The reason we know Adele's music is because we hear it on the radio a jillion times a day...and on commercials...and in the mall. The reason we know Beatles' songs is because we grew up listening to their records over and over with our friends. Classical music is no different. Those who enjoy it have developed a familiarity with it over time, either by exposure in the home, or through studies in school or private music lessons.
So does it really matter who plays a piece? That's like asking, "Does it really matter if Kelly Clarkson or J-Lo or Adele is singing?" I suppose the answer depends on who is listening.