My understanding about "Rulings over rules." is not that the DM can just ignore the rules as if they weren't there, but rather than when confronted with something vague, that the rules don't cover, or a situation where the rules doesn't make sense, he is encourage to make a ruling for that situation rather than just blindly follow the letter of the rule.
It seems to me like the DM is given primacy over the rules even in that sense. I'm not even sure "Rulings not Rules" is actually in a book somewhere, it's something Mearls has said to sum up the whole philosophy.
Anyway, 5e rules are written in natural language, so you can probably find a pretext to rule one way or another if you like, but who judges whether the rules are vague enough to require a ruling? Why, the DM, of course.
I agree though, even though we ninjas the response. I don't like the "placebo die". Where the DM secretly rolls behind his screen, but the result is already set in stone, and not affected by what is rolled what so ever. Either you roll and accept what is rolled, or you don't roll at all.
If you've decided that the assassin sneaks up on the players unnoticed, then what is the point of rolling fake stealth checks behind you screen to maintain the illusion of the rules?
That illusion can be important to some players, or, less charitably, there are players who will draw conclusions from what they observe at the table that their characters have no basis for. If you roll, the assumption is that the thing you're rolling for isn't entirely out of their league, where if you don't they might assume that it is. If what's really happening is that you decided for narrative reasons that an enemy who might or might not succeed, did in that instance, you'd be telegraphing the wrong in formation. Of course, you might also not want to telegraph the right information.
Now, that's only true of some systems and some players. With a different system and players who are up for it, you can have everything out in the open. Or you can merely keep less behind the screen. It's a matter of system, styles, preferences, and what works for the DM, at his table, possibly even moment to moment. There are times, for instance, when, even though you generally keep things behind the screen, you make a roll in the center of the table, or you tell the players a statistic off the monster's stat block. Running 5e requires a lot of DM judgement and is at least as much art and feel as 'science' or system.