Who gets posession?

[Adam]

Too late on the scorebook issue, so that should simplify who gets the ball. White won't be shooting 2.

As Nevada notes, a shady scorer could take advantage of this by not telling the officials.

If the rule was different, a shady scorekeeper could hold on to that T until an opportune time and then inform the officials, giving their team possession and two extra free throws at a crucial time.

If you think the scorer is being shady, have him/her replaced. No T can be served, though.