My previous supervisor (current coworker) was/is excellent about this. Yeah, of course the actual data will be front and center in the decisionmaking process, but he always makes a point to actually validate that data (through hands-on / direct observation or through his direct reports), knowing full well that there's no such thing as perfect data (there's always a missing metric or an unreliable source somewhere).
More importantly, he's willing to put himself behind his decisions, and always encouraged the rest of us to do the same for our own direct reports (and while I don't and didn't have any, I still took his lessons to heart): if you need to rely on / appeal to external sources of authority (be they higher-ups, data, "corporate policy", etc.) to assert your own authority, then your own authority is illusory, at best. By all means explain your reasoning, of course ("transparency is a dependency of trust" applies to any kind of computational system, including the kind that sits between our ears), but it should be clear that it's your reasoning, not someone (or something) else's.