I would not entirely dismiss the role a coach or philosophy/approach plays in RISP success. The Cardinals in 2013 were otherwordly with runners in scoring position, and some of that had to do, you'll recall, with Allen Craig batting better than .400 with runners in scoring position. And that was no small sample size. Over the course of what would have been, goodness, nearly three/four months of at-bats he was like a .350 hitter in those spots. Charlie Manuel once told me that he admired how the Cardinals "figured it out," and his point was that they were so good with OBP -- look back at the numbers -- that they could then get the defense in motion, away from the shift, and on their feet and open up spaces on the field for hitters like Craig to excel.
It was the marriage of personnel -- high OBP, hitters like peak Craig -- and approach.
It's always going to be skill/personnel > approach, because any approach is, by definition, going to hinge on that player/team's ability to execute it. And if they don't have that ability then they either won't succeed or a new approach is needed.
One thing about the current approach for the Cardinals is they don't always delineate between a RISP at-bat and an open-bases at-bat. Yes, they play the scoreboard. Yes, they need the ball in play. But the current thinking is that a quality at-bat looking for a strike in a prescribed zone and hitting it hard is going to produce regardless of the situation. I get the thinking behind that. A swing/approach that produces a double when the bases are empty also produces a double when a runner is scoring position. I'm oversimplifying but you get the idea: A sound approach at the plate is a sound approach, regardless of situation, and a sound approach begins with identifying the pitch to hit and drilling it. The disconnect that is large part personnel and small part modern hitting is the strikeout, and how that in some situations absolutely unplugs an inning when a ball in play, as Manuel, said can finds holes if the defense is in motion. A hitter looking to do what he does regardless of the spot, is going to invite the shift, or risk the strikeout and innings collapse, RISP are left stranded, offenses burst big and go quiet for stretches.