I think it's just not that cut and dried.
I'm going to side step from dogs to talk about Thoroughbred horses simply because I know them better.
Thoroughbreds are perceived as wanting to run fast. They have been bred through generations to have the physical ability and mental desire to run fast.
However, a Thoroughbred who has never seen a racetrack has distinctly less mental desire to run fast, *on average* than one which has raced. Why? Because when we stick them on the track *they get a social reward for running fast*. TB racehorses appreciate being the center of attention when they win. They get lots of praise when they run well. This reinforces the natural desire to run fast...just like a farm border collie who gets a nice pet and a treat for bringing in all the sheep gets the desire to herd sheep reinforced.
At the same time, you get the occasional Thoroughbred who's answer to being told to run fast is a big fat NOPE. I know one who was a fairly high six figure yearling, got to the track and outright refused to run. Just wouldn't do it. Didn't want to.
Breed traits are *traits* and *tendencies*. They don't establish the full personality of the animal. Ignored traits tend to be highly variable. For example, back to our Thoroughbred racehorses. It doesn't take a lot of intelligence to run as fast as you can around a level track with somebody telling you when you are approaching the finish line. Second dumbest horse I have ever known? Thoroughbred. Third dumbest? Thoroughbred. Absolute dumbest? Half Thoroughbred. But I have also met some very intelligent Thoroughbreds. The trait of intelligence is not needed and thus is not bred for and thus becomes extremely variable and it's one of the things people buying a TB as a riding horse look at.
It's overly simplistic to say it's the breed, to say it's the owner, to say...it's ALL of these things. And no matter how carefully you breed for temperament, you are still going to wind up with a greyhound who doesn't want to run, a border collie who ain't smart enough to herd, etc.