I agree that the second bit is incorrect, if assessed against the FAR. It seems to me that the FAR definition anticipates initation action before or at V1. It seems to me that the Boeing definition quoted by Leaddie anticipates that as well. Perhaps Leaddie is misinterpreting the Boeing definition?
That said, I also agree that the Boeing definition is vague. What does "stopping has ... been commenced" mean? Does it mean deceleration has commenced? I don't think that is what the FAR definition anticipates. There's a difference between initiating action to stop and that action starting to take effect.
That's why it seems that you don't 'unmake' a decision to reject, even if you exceed V1 after initiating stopping action before or at V1.