Doesn't science appear to do this as well? It models what it observes, but it certainly doesn't nail everything down. And I wouldn't consider this approach misguided.

Scientific claims are verifiable. That doesn't mean that they are true.

Religious claims are by definition and practical circumstances not verifiable since they are claims about things outside what we can observe.

But they are also claims that there is a metaphysical reality which we cannot access through science but contain truths about the world we can access. And that is where it falls apart IMHO.