Substitute Unannounced reentry Legal or Illegal

After pulling out a starter, a coach inserted a sub to bat for this starter. The sub was announced and the substitution was legal. In the 5th inning, the coach decided to re-enter his starter. He did not announce it to the umpire or the home book. The starter that was re-entered was properly placed in the lineup in the same place in the batting order.

The opposing team stated since the re-entered starter was never announced, it was not legal and therefore an out.

After reviewing the rule book(s), all I can find is about a sub entering the game. Basically, what the rule book says is that as long as the substitution is legal, the act of entering the game by the sub, that is all that is needed: Rule 3.1.1.

What about a starter re-entering the game? Does he have to be announced or is the act itself enough of announcement?