This is mind boggling.
As was quoted earlier, the actual course teaches that you cannot do chest compressions in the water. The rescue scenario that instructors are required to teach and on which they are all tested for certification does not include in-water chest compressions.
First aid courses today teach that if the victim is not breathing, then the blood is also not circulating, which is the reason chest compressions are so important. There is an exception for drowning, though--it is possible that in a drowning, the blood is still circulating. That's the hope, along with the possibility that the victim will vomit water and begin breathing quickly.
There is no doubt that the climax of the rescue course, the surfacing (etc.) of a non-breathing diver, is a serious situation. For more than 15 years on ScubaBoard, I have challenged anyone to provide a true example of a case in which an unbreathing diver has been brought to the surface and later revived after having gone through the entire rescue sequence of the rescuer removing the victim's gear and his/her own gear while simultaneously providing rescue breaths and towing the victim to safety. I have never had anyone provide an example. I have had people give examples of people who were revived after being brought quickly to the boat or shore and given CPR there, so that would be my own personal inclination.