In this situation the thing to do after everyone has thrown in their .02 is to go to the casebook.
Page 51, Rule 7, Throw-In Plane, 7.6.3A Play: "While attempting a throw-in, A1 hollds the ball through the plane of the end line. B1 (a) slaps the ball from A1's hand(s); or (b) simply grabs the ball and then throws it through B's basketball. RULING: In (a), no violation has occurred and play continues. In (b), score two points for Team B.
Therefore, using the above two examples, you can add in the third case, a held ball by A1 and B1, thereby creating an alternating possession situation.
You counter with, "but A1 is standing out of bounds when the held ball occurs." That is correct in all three cases, therefore in all three cases the ball must be alive.
Isn't it amazing what one can find in the materials we paid for at the beginning of the year