Correctable error

[Back In The Saddle]

Team fouls are 6 - 5, and at the next foul the official lines everybody up to shoot 1&1. The first shot misses, is rebounded and put back. As the other team takes the ball out of bounds for the throw in, it's brought to the official's attention that the fouls are now 6 - 6, and there shouldn't have been any free throws.

Obviously this is awarding an unmerited free throw. And it's within the correction time frame: "In order to correct any of the officials' errors listed in Article 1, such error must be recognized by an official during the first dead ball after the clock has properly started."

The question is, how do you resume. By 2-10-5 "Points scored, consumed time and additional activity, which may occur prior to the recognition of an error, shall not be nullified."

The miss and putback, to my mind, constitute "points socred, consumed time, and additional activity." So it would be proper to let that play stand. If there was to be a correction applied, it would be that the shooting team would be given the ball OOB for a throw in at the spot nearest the foul. You can't do that and give the other team the POI throw in along the baseline.

What is the correct thing to do here?