They are not 6 categories of overthrow, or they would be labeled as such.

Well, they're 6 types of overthrow, but they're not labeled as examples, either. They certainly could be examples, but it's not fully clear. If I were editing the J/R, it would say, "Some examples of overthrows follow."

Note that with altered bats, the J/R introduces its list with "Examples of altered bats include bats that are:" . . .

But for foul balls, it reads:

"It is a foul ball if a batted ball:" . . .

and then lists 7 categories that cover every kind of foul ball. (The J/R even includes "is touched by the batter in his batter's box, which is not in the official book definition). It doesn't specifically say that all foul balls fall into one of the 7 categories, but they do. These are not just examples of foul balls.

I don't expect rule books to be written like law books, and I can accept that the play in the OP is considered an "overthrow." I'm just saying that the books don't cover it unequivocally.

Agreed. Good examples. ;)