Bagpipes theory

The other day, I ran across the myth of Marsyas, who foolishly challenged Apollo to a music contest. As generally happens, he lost. Apollo skinned him, and, in some versions of the tale, made a wineskin out of Marsyas's hide. Another version says that Marsyas's skin is hung up in a cave, and moves if you play Phrygian music near it. Marsyas was a Phrygian, and some sources suggest that the myth reflects a cultural struggle between Phrygian and Greek musical styles.

I'm writing this post because of a connection I made while Googling about this myth. Could this bag of skin that responds to music and is associated with pipes be... a bagpipe? Apparently, the ancient Hittites may have had bagpipes, so it's not completely out of the question. Could Greek culture have so trounced the acceptibility of the bagpipe that only this echo of an echo of a myth reflects its existence? It's thin evidence, but I think it's a good story :-)