In the counter he showed, the other arm is only used to counter punches. Since the off-side arm of the "attacker" is being used to control an arm, there's no need to control it - it is controlling itself. I'm still not sure the control in that method prevents the counter from the video, since the arms aren't activating anything - they are simply attaching to the opponent. When we look at the throw, getting your center low enough to give you leverage is what will prevent that counter. The arm control is preventing other counters.
The "3 points control" can only disable the arm. It's the spine bending that disable the counters. In order to do so, the "elbow joint" of your head lock should point straight down to the ground. In that clip, since he did not "crash his opponent's body structure", his opponent's left waist wrapping arm can still pull him back and down.
IMO, if
- your head lock cannot bend your opponent's spine side way, and
- your opponent's free arm wraps around your waist,
you have to
- change your head lock into over hook and apply pressure on his elbow joint,
- use your right leg to "spring" his left leg back into a bow-arrow stance.
If you want to use head lock,
- not only you need to develop a strong head lock,
- you also need to train many other skills such as over hook (head lock and over hook are twin brothers), elbow crack, leg spring, leg lift, leg twist, inner edge sweep, shin bite, front cut, outer twist, ...
