The "false grip" is what determines whether the muscle-up is an exercise worth doing, or if it's just a gym trick with little actual training benefits.
Use the false grip and you'll be able to "peak" your body by applying muscular force to the bar or rings. Don’t use it and you'll need to peak your body by relying on swinging and momentum to get above the bar.
With the false grip (flexed wrists, palms on top of the bar) you're able to dip out of the transition from pull-up to dip. With the pull-up grip (wrists neutral, palms in front of the bar), you'll have to use momentum.
Think you have what it takes to make it in the world of elite sports? Do you have immense talent and ability? Great, but so do a few thousand other guys. Unfortunately, all of these things will only get you so far in this world where good often isn't good enough. At this level you have to be one of the best just to get your foot in the door.