I understand the argument, as I have read every article on the subject posted by ARMA, and participated in many discussions on the subject. I actually do agree that forceful square-on edge on edge contact between two sharp swords will cause damage to one or both swords. I don't think that's really a debate anyone can have, given the results of a simple experiment. I also think that the flat was used quite often in various ways for defensive actions. What I'm not so sure about is the fact that systems of fence and techniques were developed around the fear of damaging the edge of your sword.
When discussing Renaissance swordsmanship, however, we really aren't talking about 19th century saber. The Bolognese school, founded by Dardi (or Bardi), who was a contemporary of Fiore specifically advocates using the edge in parrying actions. They were using sharp cut and thrust swords, with thin edges. They never mention using the flat of the weapon in a defensive manner at all. Now, we can discuss whether the edge of the defending weapon will strike the flat of the attacking weapon, perhaps it does, or makes oblique contact with the edge in some manner. But my point was that in all of the examples of presenting the flat of a sword for defensive purposes, the flat was specifically turned so that the attacking sword would strike it, not the edge. This does not really go along with what Marozzo, Manciolino, or del Aggochie tells you to do (or Viggiani for that matter). They say that you can either use the true edge or the false edge to parry. You can counter-cut, deflect with the false edge, or enter a guard that places the sword between you and your opponent's. But any way you look at it, the instructions given by the Bolognese Masters mean that you will be presenting the edge of your sword to his strike. They don't really say what part of your sword will contact his, and from my own experience more often than not there is an oblique contact, often the forte of the defending weapon taking the force of the blow (when doing the static hard stop). Marozzo's Spadona (2 handed sword) section says that there are two places you can be crossed with another sword, true edge to true edge and false edge to false edge. That sounds a lot like hard edge to edge contact to me.
In several of the images you posted John was using a Pflug guard, with his flat presented to take the force of the cut. Now I understand that this is
German Longsword, and not Bolognese sidesword, but in his book he specifically stated that Renaissance sidesword systems used the flat of the sword to parry, so I assume he does something similar with a sidesword. This directly contradicts the Bolognese school writings. Unless we aren't understanding the words of the Masters correctly, you cannot present the flat of your sword to an attack and then say you are using the true edge to parry with.
As far as Guy Windsor goes, I think he had a great section about this issue in his book Swordsman's Companion. He basically stated that using the flat to make a stopping parry instead of the edge was much weaker biomechanically, as you can observe. He then advocates striking the edge into the flat when counter-cutting or deflecting, which I agree with. He also states elsewhere that using the edge in many actions against another edge will cause damage, but that's what cutlers were for.