How quickly a dog picks up a command, how many times told, etc.

I believe its a fallacy. I believe it would depend upon the trainer and the individual dog. An exceptonal bright dog will not overcome a bad trainer. The dog doesn't pick its trainer (unlike those Disney movies). It has no control over what its taught or exposed to. On the other side, an exceptional trainer will bring out the best in a dog.

Comparing both situations, who can say which dog is more intelligent, the dog with the bad trainer (limited exposure to training) or the dog with a good trainer (that learned more)?