You are probably talking about several decades ago, when UHMS study found that CESA was the part of training most likely to lead to a fatality. As a result of that study, a number of changes were made to the CESA and especially its training. The biggest problem was the old requirement that the student take the regulator out of the mouth during the ascent, supposedly proving that they were not inhaling. This led to drownings when they did inhale. Current instructions emphasize retaining the regulator in the mouth.
In my experience, this hasn't been the case. I went through the NAUI "Basic" training course in 1984 and I was always taught to retain the second stage and to exhale with attempts to inhale to get a breath here and there with air expansion as you ascend. I became an instructor in 1987 and never heard of any special problems with CESA training. The only skill that was an issue and was debated and eventually eliminated was "Buddy Breathing" using one second stage between the two divers when sharing air in an OOA situation. There were reported a number of fatalities due to drowning while attempting to buddy breath.