This particular myth springs from a desire on the part of one author (we all know who, right?) to show how historical combat was completely different from what Hollywood showed on the big screen without actually doing the research necessary to understand the problem. Additionally, some folks have noticed that relatively few extant swords have much edge damage, thus leading them to believe edges were not used for displacement in the middle ages. There is also a certain sense of value operating here: someone buys an expensive sword and he can not imagine letting it get all hacked up, so he transfers that reticence to his medieval ancestor.
As logical as all of that might seem, careful research shows it is simply not true. Hollywood doing something does not automatically make it wrong (suspect yes, but not necessarily wrong), and most extant swords probably were not used for fighting; only the nicer pieces tend to survive. Moreover, we know swords often got hacked up; read this quote from a fifteenth-century chronicle:
"...and after the battle his sword was all but ruined. The beautifully gilded hilt had been bent and nearly wrenched free and the blade all notched and toothed like a saw" (Gutierre Diaz de Gamez, The Unconquered Knight: A Chronicle of the Deeds of Don Pero Nino, tr. John Evans, In Parenthesis Publications, 2000, p.16).
Then we look in the Fechtbücher themselves. The German sources do not say much on the subject, but George Silver does; in his “Brief Instructions” he says: “...ward his blow with the edge of your sword” (fol. 24r). You can not get much more clear than that, and he is not alone—other authors say the same thing.
Edited to add another master's instructions:
“All cuts must be parried with the edge. The reason: Because, if one parries with the flat, the parry can be easily cut aside, and thus a strike can be achieved.”-- Erhardus Henning; Short Yet Thorough Instruction on Cut-Fencing, 1658.Why displace with the edge? The fact is that while you might get a nick in your blade, you have to remember that you will normally displace with your strong and cut with your weak, so nicks on the strong have little effect on the sword’s efficacy. Worse, if you displace with the flat of your blade you are much more likely to break it. Consider a wooden board: If you strike the edge you are much less likely to break the board than you are if you strike the flat—it is simple physics.
Moreover, edge displacements are stronger than ones with the flat. Try this experiment: Get a practice sword (not a sharp one) and hold it normally. Now have a friend push against the edge while your resist, then try again with him pushing against the flat: Surprise! It is much easier to resist his push with your edge because that is the direction in which your grip is strongest. Thus, if you try to displace with the flat of your sword there is a chance your opponent will be able to simply blast through your defense.
So while you might not normally go out of your way to displace edge to edge, in many techniques it is perfectly normal; the Zornhau is a perfect example of this. And, as you can see, there is no reason to twist the principles of fighting completely out of their natural order in order to avoid doing something that is not only natural, but perfectly safe.