Watching the slow motion portion after the wheel rub and you can see the wheel wobbling at a different rate than the fork/handlebars which indicates there was a problem of some sort with the hub which probably caused the broken spokes. Break 4 spokes and your wheel is for sure going out of true. With the wheel wobbling like that, I would imagine that any amount of front brake could cause them to suddenly grab. If a wheel goes far enough out of true it could grab without applying any front brake at all.

Also note that the guy's chain is adjusted with too much slack. The chain didn't contribute to the crash, but does support the notion that this bike wasn't maintained in proper working condition. I'm guessing this bike was going down eventually and we just happened to see it when it did.

I've been cycling for nearly 40 years and have never gone over the handlebars. I use my front brake a lot. I think the OP's fears are unfounded. Crashes by other means are much more common.