I must take issue with your statement. Rather than some "fact", you are really saying that period clothing is a factor in some people's interpretations of some techniques. But how much faith should we give their interpretations if it requires us to be dressed in a certain manner? If an interpretation is truely historically valid and martially sound it should be independant from any clothing. Over gripping of some modern shoes is only an issue on modern gym floors, not on dirt or grass. Plus, period shoes on modern gym floors result in lots of sliding. Sliding up to your adversary is just not martially sound!
I wouldn't say that it is REQUIRED for a certain manner of dress, merely that it is an aid in proper execution of certain techniques.
As you can see, in a more clear synoposis of my statement at the end of my post -
On the other hand, aside from utilizing the clothing to enhance the skill and understanding of the student, I do agree that there is a bit of a problem with overdoing it on the garb and underdoing it on the sword.
I do not necessarily press that period clothing is necessary for the interpretation, but it can be helpful in enhancing the skill and understanding of the student [under certain circumstances]. For instance the shoe example I gave - they would be helpful to aid proper footwork, if only a little, on, say, a grassy terrain common to the middle ages (doubtless one of the environments these techniques were developed for). As a counterpoint, the gymnasium example you gave results in the need for more modern (and grippy) footwear to prevent issues with sliding on the floor. In the latter case the period clothing does nothing to "enhance the skill and understanding of the student", and in fact would detract from it, and thus it would in fact be a better idea to not attempt to use period clothing in that environment.
In some situations, such as those you have described, you are perfectly right - the clothing does not in fact add any actual meaning to the interpretation OR execution of the technique, and hence need not be present (and in fact probably should not, in the case of that giant diaper pants getup!)