Award after throw goes dead

[nine01c]

Originally posted by Carl Childress
Here's the relevant MLBUM ruling to the play in question:

The umpire will initially award R1 home (two bases from his position at the time of the throw). But if the runner retouches first, the award becomes two bases from the time of the pitch. If after the ball becomes dead the runner touches third before returning to first, he is subject to appeal.

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I still have a few questions not answered yet.
In the above explanation, does it specify if the runner has left early on the pitch (hit and run) or just left early after the ball is batted? Does it matter? I understand Carl's explanation of this but I don't recall ruling differently in each case. Maybe that's the whole point , there are now two different ways to rule depending.
Also, the last sentence is contrary to OBR in that R1 is retouching 1B when he has reached 3B after the ball has become dead. How is this allowed? Also, isn't R1 subject to appeal no matter which base he now occupies (except 1B of course)? I guess I'm not sure why they need to state that R1 is subject to appeal here (of course he is, right?).