I'm unaware of any studies done on the topic. But I've been teaching for almost 15 years, and have been a student for 35 years. I've run the gamut from Olympic and ITF Taekwondo, to Shotokan Karate, to Wing Tsun, to Hapkido, and to Aikido.
And so I'm going with myth.
Namely, he said that humans are pretty close to naturally able to throw high kicks and fast punches
This is a joke. That's why we train - to learn how to do what this clown says we are naturally able to do.
Acute injuries, like sprains and bloody noses, are due to accidents, while chronic injuries, like osteoarthritis, are due to training methods.
Some forms of improper training - like improper warmups, stretching, or conditioning - can lead to acute injuries, which can lead to chronic ones. Torn ACL, hernia, dementia pugilistica, and Chronic Traumatic Encephalopathy can all be caused by repeated acute injuries.
I've seen dozens of people coming in from long hiatuses, and never once did they get injured because their brain said "yes" while the body said "no".
Really: who does that? Who stops training for a few years, then out of the blue comes to class and starts where he left off, raring to go? Nobody does that. They take their time, they stay in the back of class, they come in once a week. They ease into their training. Some may ease into where they left off, others fall short.
While there might be a few who've done that, the number of injuries I see are far and away caused by accidents with students who are not returning from hiatus, than by those who get injured because they overestimated their ability to return to where they left off.
In fact, it's the people who DON'T take time off from training who I see are more likely to get injured. Chronic fatigue, and boredom, lead to instances where mistakes are made because the student is not paying attention, or who is compensating for injury or fatigue.
Bottom line, though, I don't see any injuries resulting from returning on hiatus, to say nothing about a majority of injuries.