I think the one punch, one kill bit is an ideal to strive for, not an actual combat philosophy. Sort of a training philosophy, designed to improve focus and concentration on technique. It would be great to only have to strike once, but I don't know of any teacher that says you should count on somebody ever going down with one shot. What I've always been told is you do whatever it takes, however long it takes, to eliminate the threat. If it's possible to end the threat quickly, great, but be prepared to go the extra mile.
As to what Skorzeny about tension vs. breathing - I totally agree. Your level of muscle & mental tension is seriously linked to your breathing. The old masters who actually fought with their lives on the line understood this, but I think it's been largely forgotten in the last 50 years. Most of what is taught today is taught out of tradition, without an understanding of what they are doing or why. For example, breathing out, or even kiaing when striking - by expelling air and tensing the stomach & diaphragm, you magnify the power of the strike, you empty your lungs which makes it harder for your opponent to knock the breath out of you, and lastly, you clear the old air out of your lungs, forcing you to inhale deeply. One of the physical effects of panic is that you tend to hold your breath or breathe very shallow - a bad idea in a fight (try holding your breath and running windsprints). If if you expel all the air in your lungs, you will breathe in.
Which, in a roundabout sort of way, brings us back to the topic - if the one punch, one kill were more than an ideal, they wouldn't need techniques to improve/enhance endurance - it just wouldn't be a factor.
And if I hear one more "heeeyah!" masquerading as a kiai, I think I'm gonna lose my lunch.