third out caught stealing what is batter status

Question
There are 2 outs and a man on first (Kingston) and batter Thomas is batting with count 1 and 1.  Kingston on first is caught stealing 2nd base for 3rd out of inning.  Batter Thomas is replaced defensively in the bottom of the inning by Hayden (Thomas is NOT injured).  At beginning of next inning, Hayden leads off since he replaced Thomas defensively when Thomas was in middle of bat when 3rd out of previous inning was obtained via a caught stealing.  Hayden walked.  The opposing team protested that Thomas should have batted since Thomas (and not Hayden) was the batter when the 3rd out caught stealing was obtained the previous at bat.  The umpire agreed with the opposing team and called Hayden out for the 1st out of the inning.  I contend that you should not be "penalized/prevented" from making a defensive substitution for a player that was batting when a third out was obtained via a caught stealing of a base runner.  Who is correct and which rules in baseball support the correct call?
Thanks.

Answer
Jeff,

When the third out is made while a batter is at the plate, that partial at bat doesn't exist in terms of the baseball records.  The batter leads off the next inning like they were never up at bat.  There is absolutely no rule in baseball that requires that person to stay in the game and take their at bat.

The umpire was completely wrong in this case.  The opposing manager should have filed a protest at that point (and then completed the game).  Then the protest would be ruled on by the league.  The proper ruling would be to take up the game from that point (before the first out of the inning) and complete the game.

Hope this helps!

Brian