I don't think this is really true (but have not been able to downvote anything for quite some time). You can have a functional understanding of how something works (if you do A to it it makes B happen) without having a model of how it works internally. This sort of modeling is what the "theory" practicalists disdain concerns itself with, and they may do well to ignore it.

Because we have limited computational abilities, we will often do better on non-novel problems by learning a few useful patterns than by deriving everything from the underlying model. There is a reason why in elementary-school math classes we do not just give the children the Peano axioms and say "have at it".