The question: "A1's throw-in is touched by B1, who has one foot touching the
boundary line. Official rules this a throw-in violation and awards team B
the ball at the spot of the throw-in. Is the official correct?"

I believe these are the relevant citations.

4-42-5 says: "The throw-in ends when the passed ball touches, or is touched
by, an inbounds player other than the thrower."

9-2-2 says: " . . . The ball shall be passed by the thrower directly into
the court from out-of-bound so it touches or is touched by another player
(in bounds or out of bounds) on the court before going out of bounds
untouched."

9-2-10 says: "No player shall be out of bounds when he/she touches or is
touched by the ball after it has been released on a throw-in pass."

Under 4-42-5 the throw-in has not ended.

Under 9-2-2 A1 action is not a violation.

Under 9-2-10 B1 has violated.

Thus, in the question in question, ball to A1 at the spot of B1's violation.
AND, if the throw-in is an alternating possession throw-in, A keeps the
arrow.

Uh, I was working hard on answering the question . . .
 

I didn't add that I wanted critique, please. Am I right????

You're correct that A1 did not violate. However, if it were an AP throw-in, the arrow would change since A1 did complete the AP throw-in.

Uh . . .
 

4-42-5 says: "The throw-in ends when the passed ball touches, or is touched by, an inbounds player other than the thrower."

In the situation in question, the ball is touched by an out-of-bounds player, no?

Hmmm, my answer was off the top of my head, but you certainly have me thinking. Let me look. Sure sounds like you're right, tho.

Better check out R6-4-4 too, Chuck.

Re: Uh . . .
 

You need to check R7-6-1.

Re: Re: Uh . . .
 

R7-6-1 concurs with 9-2-2 in that " . . . The ball shall be passed by the thrower directly into the court from out-of-bound so it touches or is touched by another player (in bounds or out of bounds) on the court before going out of bounds untouched", meaning, I believe, that the thrower violates if s/he throws the ball onto the court and it goes out of bounds without first touching or being touched by a player in or out of bounds.

(Writing the same rule slightly differently in different places - what a concept, eh?)