Base award on Appeal overthrow

[Altor]

One thing the MLBUM ruling doesn't mention, but is probably obvious to most people on this board. Doesn't the runner between second and third also have to touch second on his way back to first?

So, if the ball went into DBT while he's between second and third, he's initially awarded home. But, he needs to touch second, then first. At this point, his award is changed to third. He again needs to touch second on his way to third.