Exactly right. It's not just isolated to karate or any martial arts. Any kind of sport/activity that requires dexterity and speed, the more tense your muscles are, the less effective you'll be. I play golf and in the beginning I thought to hit the ball far, I have to "grip it and rip it". I was shocked to my core when my teacher told me to relax and swing easy. More consistent, and I hit it as far or even further. With guitar playing, the only tense part of my fretting hand are the fingers (when I'm barring chords). But forearm and wrist are loose. It's why I have the guitar up higher than some. Having the guitar too low when I'm standing up just tenses up my whole left arm from the elbow down.
You're correct. Their contract with DPD should have included insurance. So as well as keeping your money, they could have potentially claimed compensation from DPD.