I'm not sure that true climbing can be used as a reference respect this aspect. By climbing lots you surely have improved your technique and smoothness, along with stamina, so this had surely an impact on your ability to put less effort on the fingers and get less pumped.
I know that the body responds to stimulus, so it will adapt proportionally to the stimulus we give. I don't see why moderate loads will produce the same adaption as high loads. He should motivate and clarify.
Tendons, capsulae, etc, being less vascularized take more to adapt than muscles, so a very strong muscle could cause problems to a yet not enough adapted tendon, but again I can't see the reason to what he says.
Moderate training is going to give you moderate gains.
Another aspect, is about what I read on T-Nation (yes, I read it a lot) about not training "on the nerve" too often.
The high nervous stress caused by training at the limit takes longer to recover, so it's good to train also sub-max.
Will try to search for some more info.
Briefly put, that videos are a doctor's point of view. They are over cautious obviously and aimed at avoiding injuries. This detracts from a pure sports performance advice.
Just my opinion.