Here's another perspective. Realistically, humans have just as much trouble with a position which requires 18 half turns as they do with a position which requires 20 half turns. Therefore I do not see why exactly the actual distance a position is away from the solved state should be considered "perfectly scrambled" (the first two responses mentioned this), as when I hear "perfectly scrambled", I think of the difficulty for a human to solve it...it's not like humans have a method to solve a cube optimally every time (if they can by chance solve one optimally in a fewest moves competition).
Therefore, I define a perfectly scrambled cube state to be any state which doesn't allow any extra pieces to be solved than intended during the solving process. It's a scramble which we call "unlucky" or "full-step". Since there are different human methods for solving a cube, in reality, a perfectly scrambled cube for one person will be an easier one for another person, and therefore a perfectly scrambled cube is unknowable and yet occurs frequently for everyone.
The only way to determine if a scramble is perfectly scrambled for YOU is for YOU to solve it with whichever method you use. Even then, it's questionable whether a scramble is "unlucky" for you should you have chosen to solve the pieces in one step in a different order, for example.
Therefore the conditions for a perfectly scrambled cube occurring is:
- Unique to the individual,
- Dependent on the order in which that individual chooses to solve pieces in each stage of the solving process he or she uses.
I therefore can understand why the first two responses were mentioning God's number, as that is the only answer which can solidly answer this question, but I do not believe the two are related. Therefore I have answered an inexact question with its corresponding inexact answer.