phil_r_58, nav points aren't fit over style so it probably wont be that, you can get this carbon lifting as geoffretired said could be off the cutter, but most probable cause if the dropping incedent was eliminated would be the removal of the doughnut of hot melt glue that forms around the shaft and pile, if it is left to fully harden and then prised off in the wrong direction ie. down the shaft the fibres will be lifted off with the glue, for future reference get your thumbnail behind the glue on the shaft side and scrap it off in the direction off the pile,
as for are they safe to use,
yes 
they are providing before you shoot them and I have done this on several occasions fill the offending area with a drop of liquid super glue then tightly bind the area with
waxed dental floss, after an hour or so remove the dental floss and just fill the area with more super glue layer at a time 'till its level or slightly proud, a couple of shots through a straw boss will rub it down sufficiantly level again, It is also a good idea to put a ring of super glue around each pile, on any new set of arrows this fills any gaps between shaft and pile and prevents more potential fibers from lifting when shot into hard straw bosses. Any bond between the shaft and the pile with the super glue will be weekend enough by the usual heat method of point removal.