Well, "over the handlebars" is not familiar with me. Losing the front is more familiar. Unfortunately this is not a myth.
Now. Before you forget the right to free speech and start vehemently expressing (assholingly shouting in writing (for the less educated)) your displeasure of that daring comment.
Let me explain.
For a riding noob, on a bike with awesome brakes, an ungentle application of the front brakes can easily cause the front to wash out. Same with trailbraking, except that can cause the rear to lose traction. Harsh use of throttle on a powerful bike can cause the rear to slide. Therefore it is right to teach braking while upright to noobs.
Now. For more experienced riders, braking into a corner, and using the throttle before the bike is upright, is normal. But more experienced riders know (or more accurately, have spent years developing a feeling for) when that is safe to do. That knowledge takes into account the bite of the brakes, the power application of the throttle movement, the grip of the tires, the surface of the road, the weather conditions. It is easy to forget that noobs do not have years of experience and easily become overwhelmed when having to deal with all that. So it's safer to teach them to be very gentle on the front brakes and only use brakes and throttle when the bike is upright. The aim of most riding schools is to create safe riders who don't kill themselves in the first weeks.