The boss is probably getting other non programmers trying to listen to music, jobs where they just can't listen and work. Like maybe sales, or customer service (I mean while your talking to customers). And then they say "well the programmers get too". So, the default easy fix is to say, "nobody can listen to music".
Personally I've found that with regards programming, listening makes all the difference in the world to my productivity. Not just any music though. It has to be something that's not to distracting. I like progressive house, trance, downtempo, etc... stuff that's not too lyric heavy. I'm sure that would be similar to other types of music too (classical, jazz whatever you like). I find the lyrics in other types of music (more main stream rock, pop, country, etc..) more distracting. Even, then it's way less distracting than the office chitter chatter. If I'm not listening to music, my attention seems to reach out and latch on to whatever conversations others in the office having, and that causing me to lose my programming zen.