I also feel like people forget that dogs understand us and themselves more than we do them.
Dogs may read our body language but I don't see how they understand us especially more then we understand them. Do they even understand themselves? They seem like they are driven by instinct much more than any understanding.
You can romanticize all you want but you can't prove a dog understands us more than we understand it.
I think a well trained dog is a dog that is well trained to do something.
It might be a blind dog, a service dog.
It might be a calm pet with great manners.
It might be a guard dog or a protection dog or a sports dog or a tracking dog, etcetc.
Each field has a different gauge on what is well trained and what is not