During testing of a pension calculator I built, the users expressed more trust in the page when it took about 5-10 seconds to show results than when it showed them instantly. They equated instant results with a less complex model.
I've always considered this a good example of the rare case where metrics are true and meaningful (how the users feel), but should still be ignored in favor of principles (well, not ignore - one should look into other avenues to improve the user's perception of the tool). A more black-and-white example would be dark patterns that demonstrably increase user retention.
