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Running is part of my regimen and I am quite sure that I could not run my best race without breathing through my mouth and nose

I talked with a good friend of mine from CA last week and about this very subject. He's now a Chinese Acupuncturist/Herbalist having completed a 4 year program and now state licensed in CA which is no easy task.
He also holds a Masters in Exercise science and before his career change, he presented and fitness workshops thru ACE and other credited fitness providers. He has workshop certificates out the whazoo for everything from weight training to running gait analysis as well as for body work techniques. He also was one hell of a aerobic teacher/fitness trainer.

I knew he would be interested about our breathing discussion.  He told me that at a certain level of intensity, you will need to mouth breath as well as continue to nose breath to get as much oxygen as you can into you lungs to starve off the build-up of lactic acid as long as possible. It's a involuntary response that you can't control as your body is " gasping" for oxygen as your pushing to and beyond your aerobic thresh hold. The longer you can breath thru your nose and exercise intensely the better off you'll be and the longer it will take to for your body to demand you start the intense mouth breathing  that will come eventually.

Excessing in intense bursts or at a high level for as long as you can is one of those examples.  KF must be very fit, as mainly elite athletes can do it and recover and go again. Once your at a certain aerobic fitness level, you need to push beyond what would be prudent for the "average" person to see any real gains. My friend has worked with some high level athletes and what they do to be the best the average person could do or would any gym allow it's personal trainers do for their customers for fear of liability lawsuits in event of injury or death.

It's not really a either/or proposition. You should breath thru you nose and the links that talk about why in regards to running, do tell you that you might " backslide" at first, bu that eventually you'll rebound and be better for it. All out intense workouts till " total exhaustion/puking" are special cases.