What is the training? I read that when that happens, take a deep breath and let yourself sink. The "drownee" will let go and look for something else that floats.
When I took scuba lessons in the Navy, the first lesson was on helping a drowning person There’s a method to break the person’s grip, work your way around behind them with your arm around their neck and your hip in their back. Then you sidekick to shore, pulling them. I was less than good at it. Nowadays I’d do exactly what you suggested...take a breathe and sink.
You get behind them then use your arm to put him in a head lock with your elbow under their chin, keeping their face above water then start swimming a side stroke back to safety.....
The main thing is to not let them grab hold of you....