Stephanie and all,
My grandmother was a very experience quilter, and a good one. She used often used low thread count muslins and feedsacks. She also used wool batting. Her quilts didn't have bearding problems at all. She did not machine quilt. Your suggestions regarding blunt needles and tension seem a more reasonable explanation to me.
Regarding the suggestion to use spritzing with anti-cling products because of static and 5-sided molecules-- it sounds like a possible scientific solution, but not one that would work with my bearded quilts. The fibers are not laying on the quilt due to static like dog hair would. They are attached inside the quilts and coming through the fabric to the outside (high quality fabric) and, incidentally, not only through the holes made by the machine quilting.