Having had specific training on this and many other driving scenarios (Honda Marysville OH has a GREAT training area....), you usually want to give slight power when a front blowout occurs IF it helps in controlling the vehicle. Every vehicle and scenario is different. Never mash on the go-pedal. Never, never, never hit the brakes. Slight power application is recommended if you are pulling a trailer, or have front wheel drive, then coast down to lower speed and pull off.
The Michelin video is good, you'll be OK as long as you don't hit the gas so hard you attempt to accelerate, or hit the brakes, or otherwise cannot control the vehicle (lost control of the steering wheel, shifting load, etc). BTW, the controlling interest in these types of videos comes from their legal department. It may or may not be the best advice, but the advice that is defensible in a law suit.