Training doesn’t start until the dog is mature enough to truly learn
Balderdash! And the rest of your post refutes this statement anyway.
What I think you are really trying to say, and what my experience points to in training dogs at the highest level of agility, is that while puppies can certainly learn, they have difficulty with impulse control until mature. So while your puppy may "know" commands and seem trained at a young age, they aren't reliable until they are old enough to have good impulse control. Complex behaviors and those geared against a dog's natural drive may take until the pup has more than the attention span of a gnat to become truly "learned" (we use the term "proofing.")
I start my puppies in their ground work agility training at 8 to 10 weeks. To say they aren't learning at this age is utter nonsense, not to mentioned they are being house broken by me and taught doggie social manners by the older dogs. By the time they are able to compete (18 months in AKC), they know pretty much everything they need to be agility dogs, but that doesn't prevent wild, out of control runs at first. Because it comes down to impulse control, which some dogs develop younger than others.