The degree to which this technique works definitely does depend on the rim/tire combination. On my Friday I have an aero Sun rim on the front with an IRC 1 1/8" tire and on the back I have a non-aero Sun rim with a Primo Comet 1 3/8" tire.
The rear tire is ridiculously easy to get off the rim - just deflate, grab a section of tire and pull and it comes right off - no tools or special technique needed. OTOH, the front combination is much harder. Even though I've already gone to thin tape replacing the rim strip and use the technique shown to get the bead into the center of the rim I still have to struggle a bit with tire levers to get the tire bead over the edge of the rim. My other rim/tire combinations all fall somewhere in between these extremes. I have always used the technique shown to make it easier and am usually successful to getting the tire off without tools but there are exceptions.
I got recently a new bike and it came with non name ("Silver alloy, CNC brake track") single wall 406 rims that have a deep and wide channel. When I deflate the tube, the tire comes off easily, no tools required.
With the Alex DM18 that came with my old bike, removing the tires was a struggle, even with tire levers.
The Alex rims are double walled and I guess that this considered to be a feature but I prefers the new rims because it is so easy to remove the tires and the channel keeps the rim tape in place (with the Alex rims I had to use Vello Plugs because the tape was shifting to the side).
Conclusion, a no-tool tire removal is possible, at least with some rims.
Now that I think about it, the Scorchers that I could not fit on my Alex rims few months ago may fit on the new rims. I will give it a try.
Edit: I put the Scorcher on the new rim using Jur's method. No tools, no sweat no tears. With the old rim, I could not fit the Scorcher even with levers and Var tool. The choice of rim seems to make a lot of difference.
"Hildy", a Novara Randonee touring bike; a 16-speed Bike Friday Tikit; Dahon Curve D3 folding bike; a green around-town cruiser; and a Specialized Stumpjumper frame-based built-up MTB.
I've been able to remove tires on my Curve's 16" rims for a while now, but I still find it easier to use a tire lever. I'll try this method next time i change a tire. (Shame I didn't see this a day earlier, I swapped on the knobbies last night for the snow.)