Sure it is! You just haven't been paying attention. :-)I play piano, too, though not very well yet.
I am barely intermediate. I can pull off a few concert pieces -- like Clair deLune and Chopin preludes but I'm far from "good." (that is, people who don't know crap about classical music think I'm pretty good. That really doesn't count.)
LOL! That sounds about where I'm at :) For instance, I taught myself to play Mozart's "Eine Kleine Nachtmusik" but without the chords :)