Well that's not quite true. The point is, I believe, that vocals are generally put right in the center of the sound-stage, so they play equally in the left and right channels. Thus right - left is most of the rest of the song, but the vocals cancelled each other out.

However, the right - left mix isn't exactly the song minus the vocals, it's an odd off-version, so subtracting that from the original song will leave mostly the vocals but with artifacts from the difference between the song truly without vocals and the right - left mix's interpretation thereof