While both videos show someone going over the bars, neither one is just regular braking. In the first, the girl was taking her helmet off so only one hand on the bars and that hand/arm was probably not holding her weight back so when she braked all of her body's weight moved forward which then tossed her. In the second, by the time the guy goes over the bars he's lost 1/4 of his spokes (at one point in the video someone says 4 of 8 spokes on the one side of the wheel), possibly has a loosened skewer, is riding on the shoulder in a loose surface and his heart rate is probably hitting 300 knowing he just saved himself from hitting blacktop at 35mph.

Thanks to reading threads on BF (silly me) and reading some other info, I've gone to using my front brake almost exclusively on dry, smooth pavement. I've found it makes riding/stopping more stable and controllable. I generally only use the rear once I'm below 10mph and coming to a complete stop. As has been mentioned, braking in wet or loose surface conditions requires more balance between front and rear.

Only problem I have is I ride on the road 5 or 6 times a week but go mounting biking 2 or 3 times a month. Off road, using only front brake is a good way to wash out your front wheel and get into a lot of trouble (while giving your buddies a good laugh).