From the article: "A faster rise of the optical acceleration above the detection threshold may outweigh a possible initial step in the wrong direction. Making an initial step forwards is not only easier than making an initial step backwards, but might also be a better choice."
It seems that the motto and the reasoning from the article conflict.
The motto exists because our basic reactionary instinct on a fly ball is to run inward, which is supported by the finding in this article.
But running inward is not a better choice from a baseball standpoint. For one thing, if you take your first step back and then recalculate and realize that the fly ball was shallow, it's easier to make up more ground and run forward. If you were to take your first step inward only to realize that the ball is going over your head, it's much harder to turn around and pursue it (yes, that fraction of a second adds up to a lot in baseball).
Also, if you mistakenly take a step back and it turns out the ball is going to fall in front of you, that means it was hit less hard than expected, which means it's more likely that the ball will be taking a friendlier trajectory (in other words, less of a line drive), and so you'll have more time to make up for your misread. In the opposite case, that means the ball was hit harder than expected, making it even less likely for you to recover. Additionally, if you make a mistake and let a ball drop in front of you, that's a single, and a relatively contained one at that as you'll be charging the ball when it lands and have the momentum to make a good throw (to nail a runner at the plate, for instance). However, if you make a mistake and a let a ball get over your head, that's a double minimum, and you'll be running away from the bases to pursue the ball, making a throw that much harder (and of course you'll be farther from the infield as well, but that was by definition).
A simplification of the problem would be to assume that you have a 50/50 chance of guessing right on whether to move in or out on a fly. If that were the case, the potential loss in mistakenly taking the first step inward is much greater than the potential loss in mistakenly taking the first step outward. In practice, there are many other factors that shape this "decision" (or developed instinct). One such thing is the sound made when the bat hits the ball (hard to explain this one if you haven't played baseball, though suffice it to say it has something to do with how loud the sound is). Another is the depth you're playing at originally. On many high school fields, which are smaller than major league parks, it's quite plausible to play at a depth where if you take your first step back, you'll catch all but the hardest hit drives, some of which are home runs anyway, and still be able to recover on misreads and catch all but the luckiest of bloopers.
If you're trying to compare the difficulty of the sports, nobody would argue that the catches in that video are more difficult than a fly ball. However, there are plenty of difficult catches made everyday in the major leagues. And hitting and pitching are significantly harder in baseball.
