How soon on a correctable error?

[Brick43]

I understand the rule says an error must be corrected no LATER than during the first dead ball after the clock has properly started but how SOON can you correct?

I had a game this w/e. A foul is committed and the table said we were not in the bonus. We put the ball in play. No sooner does the ball get in-bounded does the table admit fault and say it is the 7th foul. The ball is live and my original thought was to blow the whistle, stop play and award the free throws. But I waited until the first dead ball.

I am reading the rule book and the case studies but they all discuss the error being found during the 1st dead or later. SO I don't see anything that says I did this incorrectly but I was so tempted to call the play dead. Then I got to thinking how soon is too soon?