Correctable error question

[Adam]

Here's my hypothetical situation:

Following a basket by A1, but before the ball is at B1's disposal for the throwin, B2 shoves A2.
Lead calls the Tech.
For whatever reason, the Trail thought the call was a live ball intentional personal foul, and informs A2 that he must shoot the free throws after A3 informs him that he will be the shooter.
Immediately after missing his first free throw, coach notices the wrong player shot the free throw and requests the error be corrected.

Does this qualify as the wrong player being awarded a free throw? Is it correctable, by rule?