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.