During training as a firefighter many decades back, a trainier from the local electric utility gave us a seminar on safety near wires. Included in this was a video, in which many actual deaths were captured (by news crews, I expect) which certainly did not make it to the public. It was terrifying! There is so much to learn about the hazards of power line contact! I recounted this training to those I trained in the fire department. I did a lot of chainsaw training too. Yeah, you have to have a lot of confidence in the common sense of the trainee, 'cause you can't account nor even train for all the stupid things you can do with a chainsaw. I've had to yell "freeze" a few times. And firefighters use chainsaws in places they do not belong - like on roofs for ventilation during house fire attack - often at night. Fortunately, when I have had to use a chainsaw on a roof, I've usually had a ladder truck or aerial platform close by as a support, or at least stop should I slip. After that, regular, and appropriate use of a chainsaw - with feet on the ground - seems much less traumatizing! But never take them for granted, particularly slicing around where you cannot see what's there really well!
All that said, in 28 years on the job, I saw circular saws and lawnmowers as the greater hazards. I don't recall a medical call attending a chainsaw injury, but I have picked fingers and thumbs of three different patients out of the sawdust to accompany them to the hospital, and pieces of hands and feet from lawnmowers and PTO's. At the end of the day, it seems that the hazard is there to be found by the unwitting in many machines - stay one step ahead while operating, and considering the operating environment!