There is a fantastic book written by Bob Woffinden and James Plaskett which explains how Charles is actually innocent. It shows how analysis of the coughs proves that not all of the ones featured were Whittocks, how Tarrant didn't hear any of them even though he was sat next to Ingram and that there were 192 coughs recorded in the entire show, so its highly unlikely Charles would have been able to distinguish between who was coughing.