I have never seen that technique, I had one season with a LOT of flats so I got the whole (flat fixing) procedure down to under five minutes (including inflation).
I seldom mount new tires as I think it should be included in the purchase price at the LBS. So I was a little taken aback by the installation of the tube before mounting the tire on the rim, when I fix a flat I only take one side of the tire off, so I guess I'm just used to slipping the tube in after one side is mounted. I will have to try both the "squeezing the tire" and "tube in tire before mounting" procedures to see if I can improve on my technique.