There is no lack of reading material on this. It's not that they don't ever matter, it's that some things we think of as obvious aren't true. And yet some of them are probably are.
Bill James actually tackled this fairly recently and found that yes, you want your best hitters in the middle of the order (though not necessarily where you might think exactly - the analysis he ran says your best hitter should definitely be 4th not 3rd.
This one takes the straight, "hit your three best hitters 1-3" argument.
This one from 10 years ago says batting order can make a difference of between 5 to 15 runs a season, which is not insignificant. I mean, we often say managers don't matter either, or might only be worth 1 or 2 wins a year at most. And the same is probably true of batting order. But 1 or 2 wins might actually mean something!
Of course this is also a fairly specific discussion. It is probably true that Kyle Schwarber should be hitting 3rd through 5th (and even the loss of ABs from hitting 5th would still be offset by his increased productivity). In this case Girardi and Thomson simply valued consistency and the comfort of the player (and he wasn't a bad leadoff hitter) over looking for a better solution, or thinking it mattered to have a fast guy (I don't think it did, but he definitely didn't drive in as many runs from there).