I think it didn't fit because, to respect the story, it should have been right before UATW ("we are meeting for the first time
"), but musically speaking, it would have probably fit somewhere else (from what people have said several times, between UFO and POC, I believe
). Since they really wanted to make a cohesive album, they couldn't put MTM, because they would have had to sacrifice either the cohesion of the story or the cohesion of the music. That's only my guess, of course.