The idea of categorically keeping the rear tire locked to a full-stop (once started) is overstatement. If you’ve not gotten sideways, immediately let off the rear brake. If somehow you’ve gotten sideways, then keep the rear brake on (to avoid a high-side) until you’ve steer-corrected and are tracking straight, then let off the rear brake immediately – looking where you want to go, not down.
That video is misleading. What the officer is doing in the video is a common balance exercise (in this case utilized to compare stopping distance – not instructing you to keep locked up brakes on to a full-stop). You can do a similar exercise by locking the front brake on a motocross bike (or a mountain bike) on a hard dirt road. Tricky stuff that!
It is best to instruct beginners to not use their rear brake at all, until you’ve learned to use it sparingly, and properly, for balance – and only then for things like trail braking into a corner.
I race on the track and ride my moto pretty much daily and very rarely even use the rear brake, except specifically to balance the bike – not to stop. I literally consider the rear as zero stopping power. My front brake is for stopping. The rear is for balance. The point – teach yourself to never jam on your rear brake – especially in an emergency situation where it’s been “proven” you can only focus on one brake at a time (and you don’t want it to be the rear – as the video shows.)
Practice emergency stops via this method. Learn what you can do. Become confident in what you can do.
Gravel is an art. MotoGP guys can hit a very soft, foot deep, gravel trap at 120mph+ and – by not using their brakes – wade through it upright and recover. Basically you do exactly as @worriedguy says, which is aggressively jam on the (front) brake as long and hard as possible on the tarmac (subject to lean angle), and then coast through the soft stuff.
[If you’re good enough, you slightly use your rear brake to keep weight off the front fork.]
If you’re going to hit something very hard and unmovable, it can be better to lay the bike down (to try and scrub as much speed as possible) if you’re already skidding through gravel. Again, as @worriedguy points out – it’s all about scrubbing speed before hitting anything or getting out into the weeds.
Now – if you’ve just had a tire blowout – you’re in a world of shit – because you’re already on “loose stuff” – and thus should not use your brakes at all until you can gain some semblance of control of the bike, then slowly brake, if you can.
A blowout on the freeway is one of the scariest butt-puckering things you will ever face. This is the primary reason to keep the proper and full air pressure in your tires, and to check them regularly. It is extremely dangerous to not run the proper psi on the road because of potholes.
Sure, get off the road if you can, but do not endanger yourself doing so. With a blowout, you’re better slowing down significantly going in a straight line and trying to control the bike vs. turning at all or purposefully veering off the road into soft stuff. The cars behind you are scared of motorcycles anyway. They will have distance and be watching you. Do not worry about them. First worry about getting the bike under control. Second, brake slightly, if you can, while maintaining control in a straight line. Lastly, get off the road safely.
The good news is that most flats are relatively slow. If something feels loose, check it. It might be a tire getting low from a slow leak from a nail.
Bikes are designed to handle with OEM sized tires. Do not change that unless you want to change the handling/turning characteristics of the bike. See this.
Have fun!