I agreed with the guy in the video for most of the talk but ...
The rear brake is your "slow speed brake": It's certainly more effective at slow speed but I use both brakes when I need to brake hard. The weight transference on a scooter isn't as extreme as on a sports bike because a lot of the weight is lower down so the rear brake has more effect. What's the point in having a brake and then not using it?
"Start with the front brake, get the feel, then brake, then use the rear": Not an exact quote but that's roughly what he said. Apart from not using the rear brake until half way through your braking, it's also a lot more complicated. If I need to emergency stop then it's much easier to use both brakes at the same time and more effective.
Use your mirrors before emergency braking: If there's an emergency in front and you need to brake hard then I suggest you brake rather than think about the driver behind. A decent rider should already know what's behind him because he'll be checking his mirrors all the time especially when approaching a junction where he might need to stop suddenly.
There is already a section on braking
here in the wiki.