To illustrate the binding, imagine the extreme case of links angle, which is the two links (upper and lower) going at the same location on the chassis, forming a solid triangle. Now imagine you compress only one side of the axle, the triangle moves up and rotates around the chassis mouting point, and at the same time the triangle tries to rotate the axle in the axle's axis (the pumpkin wants to point down, it tilts forward).
But on the other end of the axle, you also have a triangle that is not compressing vertically, and is trying to keep the axle from rotating/tilting forward. So the binding force is the links are trying to twist the axle. Having a slight angle is the same, just to a lesser extent.
I do not believe it is true that with a completely parallel setup the links try to rotate the axle, they actually only try to move the axle UP, and FORWARD which does not cause any binding, but causes some axle steer. As long as the links keep the two joints on the axle vertically aligned, the axle does not get twisted. The arms being parallel, there is no actual roll center, the roll center is infinite, thus the axle does not rotate. It is just like an double triangulated suspension, if the lower and upper arms are same lenght and parallel, there is no camber change whatsoever on the wheel.
I think what the guy has found is that if you have different lenght links up and down, or non-parallel links (when viewed from the side), you can reduce the binding (maybe eliminate, but I am really not quite convinced about that yet) by moving the two upper axles pivots down a little. When he talks about parallelism it seems like he is talking about parallel viewed from the top.
Having the upper links shorter than the lower links will also cause binding even if they are parallel, because they do become non-parallel as they get compressed. This might be what the guy is referring to. But parallel with same link lenght does not cause binding in my opinion. I am still open to read/discuss it and learn thought!
Fred