So could you enlight us all with his method?
Nope it's a secret I'm going to take to my grave so no one will ever know how it's done and will have to fix flats the slow way! LOL!
Just kidding of course!
This method only works if you know whatever caused the flat is located on the tire.
If you know what caused the flat because you can see the offending object embedded in the tire you simply remove about 1/2 of the tire on one side of the rim with puncture in the center of the 1/2; next you then pull out about a forth of the tube again with the puncture in the center of the tube; either pull out the offending thing that caused the flat from the top of the thread of the tire, or go inside and pull it out that way, regardless you need to check to make sure there is nothing left in the thread or carcass of the tire to cause another flat; then you simply patch the tube as normal, restuff the tube, rebead the tire and inflate.
Some tires with tight fitting steel (wire) beaded tires this may be impossible for for loose fitting wire beaded tires and folding tires, even tight fitting folding tires, it's easy to do. Obviously if you can't find where the hole in the tire is then you'll have to remove the wheel off the bike and remove the one side of the tire and take the tube out to investigate to find the leak and fix or replace the tube.
I would say I can fix roughly about 50% of my flats without ever taking the wheel off the bike.
I've been able to make that process even a bit faster by using glueless patches, if done right good quality glueless patches like Park or Lezyne will work and hold for the normal life of the tube.
So how are glueless patches done right you scream? simple actually, you just prepare the tube as you would using glue on patches, and that means buffing the tube; then cleaning the area with a alcohol pad; then remove the patch off the backing by touching the smallest part of the patch as possible, usually a corner; lay the patch so that the hole in the tube is about in the center of the patch; press the patch as hard as you can between your fingers and thumb for about 30 seconds, look at the patch for any frosty areas, if you see a frosty are repress that area for 30 seconds and check again for frosty areas; that's it. I've been using glueless patches for over 20 years and only had two fail, my first one I ever put on, and a cheap one I bought called Scabs if I remember correctly didn't hold air for more than one day.
As an emergency, black Gorilla tape cut to a square will fix a flat on high pressure tires and hold for about 2 days if you prepare the tube correctly as I mentioned above; this black Gorilla tape might hold longer on low pressure MTB tires but I haven't tried it with those to know how long it will hold.