Hi TC... What you will find is that the lever, cables, and interface to the brakes are all independent from the hydraulic brakes, but the mechanism for compressing the pads is a mechanical part of the stock calipers.
So it's not "completely separate", only about 85% separate....
In this picture you can see the eccentric lever that the cable pulls on to compress the pads mechanically.... (of course this was before my brakes were cleaned and refurbulated…..)
Rocky