The way the leads on this capacitor type mount, the joints have the least strength if pulling straight up (will want to separate the pads from the board, but have the most strength if you pull horizontally along the length of the solder joint.
If you twist the top of the can off above the plastic base, the majority of force is along the horizontal (guided by the plastic base) and either the pins break off in the metal can, or right at the edge of the pads - either case is easy to clean up with flux and braid. Haven't had a lifted pad failure with this method ever.
That said,I haven't worked with boards in as bad a condition as was shown in the video. In those cases hot air would seem better, but I'm not sure if you'd be left with good pads/traces in any case.