It's interesting reading this thread soon after the "why do musicians work for free" thread. I have some friends who made their living for several years playing exact reproductions of famous rock songs. They toured glitzy lounges. It was their job. When they weren't at work, they played whatever they felt like, mostly music with little or no income potential -- folk, blues, jazz. They had a skill that allowed them to use their passion to make a living. So on the one hand they had the "shame" of playing covers (what a stupid concept!), but on the other hand they didn't have the "shame" of playing for free (another stupid concept).
In my case, I've tried to play exact reproductions just for the fun of it but have always failed miserably. I can get the notes right, but I always seem to insert too much of myself into the interpretation, and I can't bring myself to spend the time getting the electric guitar tones just right or the finding the correct synth voice. I also improvise a lot no matter what kind of music I'm playing and flights of fancy are usually much more interesting than the existing arrangement.
There is a real skill to playing exact covers, and it's one that many musicians don't have or haven't developed. Perhaps we should extend the OP to say that if you can't reproduce a piece of music you also aren't really a musician . . .
I've also heard that if you can't read music you aren't a real musician, if you always read music you aren't really a musician, if you can't pick up tunes by ear you aren't real, if you can't harmonize you aren't, if you can't sing you aren't, if you don't play an instrument you aren't, and that drummers aren't real musicians. These concepts are all as stupid as the OP.