I've been this way my whole life. I had to have the TV on (or talk radio) all through grad school so I could focus. Music actually distracts me more and makes me want to get up and dance.
I ALWAYS have the tv on when I'm turking. I'm more distracted if I don't have the noise in the background.
Don't get me wrong, I love me some silence, but when I need to focus I need noise I don't have to pay attention to (don't talk to me, I can't tune that out! I broke up with a dude in grad school who couldn't understand how the TV didn't bug me, but him talking right at me did...seriously?)