The overkill meaning is to have absolutely no breaks in the copper layer under the module what so ever
The more realistic approach is to ensure any fast signals do not cross any breaks in a ground plane where possible, and to plan your return currents to make sure they can follow your signal.
E.g. you have 2 signals that cross on the top and bottom layer, well the return current on a high speed signals wants to be as close to the signal trace as possible, generally following it on the ground plane underneath the signal, you have to allow a way for that return current to follow that signal past where it crosses the other to prevent it detouring around, which makes it both more likley to radiate noise, but also be suseptible to it.
One approach would be to provide some via stitching around the crossing so each return current can jump to the other side, adjacent to the signal, continue past the break, then jump back down. its not perfect, but its far better than the alternatives.
At higher speeds these breaks would also appear as impedance mis-matches, as the return current has to pass through a higher impedance per unit length of signal trace.
And to set the concept straight in your head, generally when the voltage changes on a pin, there will be a current loop formed, from that pin it likely goes to the supply rail of that chip, through your voltage rail, to whatever other chips supply rail pin, then completing on its input pin.