Courtesy Runner

[harmbu]

Last night in a FED game, the opposing team took the lead in the top of the sixth when their best pitcher (who had been playing shortstop) got a double to drive in the go-ahead run. The coach wanted his pitcher to warm up to take the mound in the bottom of the inning. He told the umpires that he was going to change pitchers and that he wanted to use a courtesy runner. Both umpires told him that he could do so. I told them that I did not think this was legal since the player in question was not the pitcher when the inning started. The coach simply pinch ran for the player and re-entered him to pitch in the bottom of the inning.

Please give me a rule reference as to whether I am right or wrong about this situation.