I'm pretty sure, given the way the specification is worded, that we're talking about two different kinds of ground pins in the connector. The implication is that there are "chassis ground" pins that are connected as directly as possible to the chassis, and that these pins are completely isolated from all of the other pins in the connector, including any "signal ground" or "power return" pins.
Further, this implies that there can be no components connecting signal ground to chassis ground, with the possible exception of a low-leakage capacitor.
In other words, the "active" ground plane of your circuit board (the one that the power and signals are referenced to) must NOT be conencted to the mounting holes (and thereby to the chassis). Only the chassis ground pins in the connector should be connected to the mounting holes, and the copper paths that accomplish this need to have sufficient clearance around them relative to any other copper or components on the board.