Correctable error?

[Rev.Ref63]

After a held ball, 'A' gets the ball due to the possesion arrow pointing in their direction. After the ball has been put into play, the arrow switched, on the next dead ball, the time keeper imforms the official that they forgot to switch the arrow resulting in the wrong team getting the ball.

My response was that it is not a correctable error and that the arrow remain where it is. I could not find a rule or case that backs up my statement. What do you think?