It could be because the player that came out of it looked like this:

Strange choice of color. . . and there had to be a connection. Engineers have a sick sense of humor.
And here I'd figured they were going for "Earth Tones" to contrast with the sterile white plastic of the iPod. Granted the iPod Mini had colors but they were mainly toyish pastel colors.
Maybe Microsoft was making a bold statement in answer to UPS: "Here's what brown can do for you".