Discard pile in Gin Rummy after a run mistake.?

During my Co Workers turn he played K,J,10. We did not realize this mistake till my turn and he had discarded. The argument was that he had to pick up his mistake. He also wanted to pick up his discard card which would be advantageous to him. The other 3 of us said he could not do that. We couldn't help he made a mistake and that the card had to remain discarded. We also said that in the event we messed up that we would have to deal with it as well, which had happened once or twice before already with no issues. This player was new to the game and refused to put the same card in the discard pile. Should he have left his original discard card in the pile or been able to choose a new one?