Ripping fabric on the crossgrain (selvedge to selvedge) does considerably more damage to the ripped edges than ripping fabric on the lengthwise grain (parallel to the selvedge). This is why crosswise rips result in much more rippling of the edges than lengthwise rips. One can accurately assess the depth of the damage from the rip only under a microscope, as most of the damage is not visible to the naked eye. Under a microscope, the damage to the fibers becomes more visible.
Exactly how much damage is done to a fabric ripped crosswise probably has more to do with the individual fabric's weave, tightness of weave, thread count, etc. than with whether the fabric was ripped in a single layer or a double layer. However, ripping a double layer is probably more rough on the fabric than ripping a single layer.
In my opinion, there is no correct way to rip fabric on the crosswise grain if the fabric is to be used for quilting. This is because crosswise ripping results in an unnecessary loss of fabric integrity. Because we want our quilts to last a long time, integrity of the fabric fibers is important. No one wants some patches in a quilt (or a joining seam for the backing) to give out earlier than the rest of the quilt. Straight-of-grain is much less important in quilting than fabric integrity.
There are instances when ripping fabric is fine -- when making rag rugs, for example. For garment sewing, though, when finding the straight-of-grain can be important, I was taught to pull a thread and cut. Ripping is simply not as good a method. The only positive thing to say about ripping is that it is fast.