Double checking on the KH Wiki (I realize that is user-edited thus can be fallible), it would seem you are both right. When a person's heart is taken and a Heartless is born, then in the Twilight/In-Between realm there is a Nobody born. Because the average heart is not that strong, the resulting Nobody will not survive long (rather vague: either it ceases to exist because it is weak-willed or it is killed by other Nobodies). The stronger the heart, the more human-like the Nobody. The thing is that the strength of the heart is not a quantitative measurement (though I am sure Terranort would have tried to measure it) but a qualitative one. It directly correlated to the will. The stronger the will, the stronger the heart. Also, this degenerative nature of the Nobodies would correlate with the threats by Xehanort's Heartless to the Org. XIII members of turning them into Dusks, etc...So the reason why an average person can be restored after their Heartless is defeated is because their heart was rather weak so their Nobody didn't survive the transition anyways.