[AtlUmpSteve]

Read ASA 8.2-F(4).
Read NFHS 8-2-6.
Read NCAA 12.2.13.

In every case, the batter-runner is out for making contact with a fair batted ball.

Now read ASA definition Foul Ball #4.
Read NFHS 2-25-1-f.
Read NCAA 11.5.1.

All of these describe a batted ball that hits the batter while still in the batter's box.

In your play, the batted ball did not hit the batter; you described the batter-runner contacting the fair batted ball. The batter's box does NOT APPLY TO THAT RULING!!