The difference in approach for the two first aid examples may also be due to the different risks involved in a fainting spell and an overdose of epi. But we digress.
As for the lapsed PPL, I think I would have done something similar, and I can only hope that I would do it as successfully as GtE has done. I haven't had any engine issues yet (fortunately), beyond some carb ice that was quickly removed after applying carb heat. Had the pilot started off on handling the emergency I might have left him in control, coaching him wherever necessary and remaining on standby to take over at the first sign of him being unhappy with the situation. You can often spot pretty quickly whether a pilot is able to deal with a situation at hand. I wonder if the signs of him operating towards the limits of his capacity weren't there already, however small, prompting the decision to take over.