Do I understand this properly to say that if the stopped simulation had been derived from the save file state using non-deterministic or control-console inputs, inputs that are not duplicated in the restarted simulation, then harm is done?

As I understand it, yes. But the harm might not be as bad as what we currently think of as death, depending on how far back the restore went. Backing one's self up is a relatively common trope in a certain brand of Singularity fic (e.g. Glasshouse).

(I needed three parentheses in a row just now: the first one, escaped, for the Wikipedia article title, the second one to close the link, and the third one to appear as text.)