I love when I get a chance to throw a wrench into a conversation.
Let's just say for the sake of the conversation, that someone comes from a place far away where there is no formal education. Let's call him Glorp.
Glorp gets a grant and enrolls in a small college and studies music theory, but the school is small and poor and has no instruments. Yet Glorp learns how to read music and relate that the little black dot on the bottom line means that he should press the first white key to the right of the group of 2 black keys on the plastic keyboard simulator. And if that dot is solid he should hold it for the duration of one of clicks he is hearing. And that the little tic tac toe symbol means that the scale uses one of the black keys and is centered around the white key to the right of the first black key in the group of 3 black keys.
You get what I am saying. A lot of us, me included if not ESPECIALLY me, place a lot of importance on the knowledge of music before we even consider the MAKING of music. So in Glorp's case, because he has no instruments available, he has no chance to apply his knowledge, but he does have the ability to, so I would call Glorp a musician even if he has never actually played a note.
Of course that is a ridiculous example, but I think you understand. In my opinion the exact moment that someone crosses the line from "I play and instrument" to "I am a musician" is the understanding of that instrument and the theories behind why the music is sweet. MOST people that I have played with that had no formal music education have acquired that knowledge by performance, and them I consider to be "members".
I was at Guitar Center and there was a mid 20s guy sitting on a small Marshall playing a Les Paul and hammering the neck with his right hand to beat the band. I walked past and asked if he could show me a Bbmaj7. He muttered an obscenity and kept impressing himself with his right hand hammering. Anybody can turn the amp up to 27 and hit strings. Yawn.