The video was interesting, but it only covered a bit of the most basic goal of gunsmithing... to be able to properly remove screws (or pins) and disassemble a gun without doing any damage.
Clapper Zapper is correct, these techniques, and learning correct tool selection, are best learned on cheaper guns than a Purdey. I'd probably also resort to the drill press method rather than the brace for removing the very tight top lever screw. Actually, I was kind of surprised he applied that much force with the brace before first resorting to a penetrating oil soak. I'd also guess that more people have a drill press at their disposal nowadays than a carpenters brace, and the correct hollow ground bits for it. I have my grandfather's old carpenter's brace and a lot of wood boring bits, but only a few wood screwdriver bits that would need to be reground for gun screws.
I doubt you would find a torque wrench or torque driver on the bench of a Purdey trained gunsmith either. Experience teaches you how much force you should apply to a given screw without stripping threads or wringing the head off. One also learns if their screwdrivers are soft or brittle, and prone to cause slippage or gouging. CZ is also correct in saying that these skills can be learned by starting at a very young age, but some never learn. I had one coworker who was very often seen hard at work with drills, E-Z Outs, and punches removing screws and bolts he broke. But usually, he twisted them off by over tightening when he was reinstalling them after a job. Most of his "T" Handle Allen wrenches looked like licorice twists.
We've all heard the term, "never a screw turned" to describe a gun with perfect screw slots. When I bought my first D.M. Lefever cross bolt shotgun, it looked like none of the screws were ever turned. But while reading an article on them in the Double Gun Journal by Oregon gunsmith Keith Kearcher, the 4 digit serial number of a gun he had all disassembled looked very familiar. I checked, and was surprised to see that he had once owned the gun I had. He had taken it apart and reassembled it with perfect screw slot timing, and not a mark on any screw. Some people can't seem to manage removing a single screw without doing major damage to the screw and surrounding metal.