This is precisely how we end up with silly rules such as the HSE arguments we know too well, people quote hearsay to expand their own personal viewpoint to the detriment of common sense and rational thinking, and all of a sudden thre epeople say it so it must be true.
Hearsay is quite a strong word. Besides, evidently a lot of people disagree that rules like "no headphones" are a "detriment of common sense and rational thinking" (as I infer you implied).
As an aside, I'm not sure why people wear headphones anyway. Obviously I understand the motivation/boredom argument. I think it's actually much nicer to run without headphones. The difficulty is, it's hard to suddenly change. But that's just like training your legs: it's tough to just go out and run for an hour (or two) just like that, it takes a little time to build up your legs to it. Similarly with coping with boredom. I used to struggle on 1 hour runs without music, now I quite enjoy 2 hour runs without it. It gives you time to actually think about things, sort out your thoughts, etc etc blah blah. It's easy to just say, "it's boring without music", but why not try, starting slowly? You wouldn't do a 10 mile run off the bat, conclude it's hard physically, and then not run again.
And with tongue somewhat in cheek, for things like marathons I agree with the previous poster that the mental challenge is to be endured/relished. You don't do a marathon 'cos it's easy, you do it 'cos it's bloody hard. So don't be a wimp and make it easier; man up and do the mental training as well. 