While I agree that this type of soap becomes harder much faster than soap produced using the cold process method, I have not yet seen any documented evidence that the soap has fully saponified by the time it has cooled down.
That being said, vast amounts of people are using the soap as soon as it has been made and they aren't complaining about lye burns or drying effects so perhaps that is evidence enough.
I'm still more comfortable with letting hot process soap cure for a few weeks first but that's just my personal preference.
The hot and cold methods of making soap are very similar, each using the same base recipes and combining the ingredients in more or less the same way.