I was directed to your site when I searched about BreathRight nasal strips. I think your article is correct in saying that these don't improve performance during exercise, but rather misses the point of these devices.
People who suffer from alar collapse have difficulty with nose-breathing. In some people the alae (the soft bits of the nose on either side below the bridge) are floppy and collapse inward during inhalation through the nose. This can be a particular problem at night. The nasal strips are superbly effective for this condition. People with alar collapse often have mucosal hyper-reactivity as well, with congestion and runny nose triggered by environmental changes - cold winds etc, and reducing the pressure swings inside the nose with partially obstructed breathing can reduce these symptoms. They help a bit with snoring, but not enough to stop me waking with bruised shins!
Having worn my nasal strip to sleep in, I keep it on for my morning jog. It helps with nose breathing at the start and finish and reduces stuffiness, but is irrelevent when mouth breathing.