Call in Indiana State Finals

[Jesse James]

Long been out of officiating, but had a question--4A finals between Bloomington South and Fort Wayne Snider. Bloomington is inbounding under their hoop, point guard touches (unquestionably, never possesses) the inbound pass in frontcourt, then follows the ball into the backcourt, hesitates, and then touches (once again, never possesses) as Fort Wayne's guard nears. Whistle for over-and-back, which was clearly wrong.....and after a three-official discussion, the ball was given back to Bloomington. I'm assuming the officials went with an IW, but with no team control on an inbounds, shouldn't they have gone to the arrow? (which they didn't).

As a hypothetical, supposing everything else stays the same (including the IW) except Bloomington's point guard grabs (possesses) the ball when in the backcourt, would that be considered POI, and the correct call would be giving the ball back to Bloomington, without invoking the arrow?