Got me thinking

[Dave Reed]

Your interpretation and reasoning is correct.

Here's what J/R says: "A nicked pitch that initially strikes something other than the catcher's glove or hand (e.g. the ground, batter, umpire, mask, protector) cannot be a foul tip; it is simply a nick and foul."

NFHS 5-1-1d says: " Ball becomes dead immediately when:.....d. a foul ball (2-16-1):.....2. goes directly from the bat to the catcher’s protector, mask or person without first touching the catcher’s glove or hand;"
Note that 2-16-1 defines a foul ball as one " that, while on or over foul territory, touches the person of an umpire or a player or any object foreign to the natural ground;"

The NCAA rule is similar to OBR.