What frays are the threads between the straight stitching and the cut edge. The closer the stitching is to the raw edge, the less the fraying will be. A double row of straight stitching won't make a big difference from just a single row of straight stitching with slightly shorter-than-normal stitch length.
I've seen some of the raw edge applique free-motion stitched, sometimes with decorative thread. That looks great too. In other words, you don't have to be exact with this method and stitch exactly 1/4" or 1/8" from the edge; you can get imaginative and free-motion as desired, even running over the edge. The only thing to be aware of is that if you don't stitch close to some edge, it will fray more than other edges.
An example of this would be a flower center; you can free-motion stitch concentric wild circles inside the center using decorative thread and let the edges fray.
In quilts that are going to be used, raw edge applique offers a different look than traditional applique. Doesn't mean it's better or worse. I think raw edge applique, at least in bed quilts that will be washed, would be better named frayed edge applique because that is the ultimate look that you get.