If I may:
Our power base is the the area above the hip bone to the solar plexus.
(If I handed someone a jar to open they would bring it to this area to open it and if it was really hard they would move it off to one side of the hip)
The last picture posted by the Professor of the throw appears to have been from a knife attack that was either taken by the cross hand or moved to the cross hand,Ill go with taken by the cross hand.
The attack is taken by the cross hand,the attacking limb is pulled towards the power base the navel or the hips,and is then moved outward to allow the victim to step into the door created under the opponents arm.
Instead of stepping all the way through and going to a center lock or forward throw,the victim stops inside the door (under the arm) and pulls the arm/hand down ,causing a cross body throw as show,but the hand holding the weapons hand does not stay far from the center ,power zone,as to make the throw and cause severe injury the hand is pulled into the center,hip or navel area.
We do not make a throw while moving away fronm the center as away is shoulder and arm power only,always towards the center,the hips or navel as the chest,shoulders,and arms are all engaged.
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The picture of the disarm and knife to the femural artery,I imagine would have come from the hip to deliver the knife between the legs as a punch or thrust and then the blade turned as the victim goes to kneeling position,and the blade would be best employed pulling from its present position towards the navel or hip.
Just my opinion based on the still pictures,I have guessed at the method of entry into these positions as they can be arrived at in any number of ways.
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If one looks at the Fight scene between Norris and Bruce Lee,(way of the Dragon)we see both have one High guard out and one low guard near the hips or center,Lee to block his lower gates and punch and Norris to punch from.
(just an example which was supposed to showcase the classical against the new age art)
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If we are in a surprise attack,which most real encounters are in street self defense,(not bar fighting),we will see that the attacker gets up close and personal to make demands,they do not stand off in kicking or punching range they are inside to avoid getting punched and to discreetly make their demands.
If this is the approach, and one was not aware,there would be not time to get into a boxing position,one would have to launch the punch,grab,strike from the hip to generate power as if you raise your hand between you and the attacker it had better be from the power zone or it will have no power.Unless one has or is given room to drop back into a good stance and raise the arms and hands to the boxers position,but I would rather drop back after I had launched a first strike from the hip or rib area,make my movement off my strike.
Again I have learned the various methods,but I do see the need to have the traditional punch from the hip or rib as distance may not be there on the encounter,so distance must be created.
Just my two cents as I do see the points made.