Typically, ground clearance is measured at the lowest point, usually the rear diff. The only difference there between the S and the OR is tires. A factory brush guard hangs low, but probably not as low as the rear diff, so while you lose "clearance" in a sense because of the brush guard, it doesn't change the basic "ground clearance" measurement.
What nerf bars/brush guards do is affect approach angle, and "clearance" under the front bumper/cowl. The low-hanging guard is another thing to hit on steep dips and also rocks and other obstacles. It's something else that isn't clear of obstacles. Factory step rails are even worse, despite the fact that they are probably higher off the ground than 9.5" (although our rockers are way low in the X). They're in exactly the right place to get banged up, and to bend and smash into the (expensive) rocker panels.
No offense to people who run these options. Just that for offroad use, they pose constant headaches.