The NCAA rule used to be different and more favorable to the batter, and there have been multiple "clarifications" of the rule.
Also, 8-2-d-2 is followed by the Approved Ruling:
A.R.—If the batter freezes and is hit by a pitch that is clearly inside the vertical lines of the batter’s box, the ball is dead and the batter is awarded first base.
Most college umpires will automatically award first on any pitch that is in the batter's box. It is hard to justify this from the currently written rule, or from the "clarifications", but real practice in NCAA ball reflects the idea the batter's box "belongs to the batter".
In general at HS level and below, there is in my opinion a high variability among umpires in the way they treat this particular issue.