In my experience the higher quality polys do not beard. I regularly use Hobbs Poly down and I have also used Quilters Dream poly. The QD I used on a handquilted project and some fibers migrated through with the quilting thread, mostly when I had just put a newly threaded needle that had a bit too much bees wax on it.
The quality of your fabric will also help to prevent bearding. I high LQS quality, densely woven fabric will also impede fiber migration.