By leaning and letting the front wheel steer itself, you can turn with hands off the handlebar. When I used a bike to go to the train station, I'd often bike without touching the handlebar for parts of the ride, including the turns. Yes, I was young and stupid.
Maybe I am still young and stupid, but I cycle a lot and as often without hands on as the situation allows... It is just much more comfortable this way.
Bu yes, also more dangerous, so in difficult trafic I usually don't do it
It's true, but in all the years of my childhood when I did this (and I rode and turned no-handed often), I never once had an accident when my hands were off the handlebars. Your warning is still useful, I think, but I also think good judgment goes a long way here.