My gun club shoots rimfire pistol falling plate matches at ranges from 15-30 yards. I've been hit many times by tiny bullet fragments, but never serious enough to do any damage - never had skin broken. But we do absolutely require eye protection, and and only a damfool would do without it. I don't know if rifles would be any worse at 15-30 yards or not. With the higher bullet velocity, the splatter might be a little worse, I dunno.
I also shoot smallbore silhouette and rimfire rifle falling plates, but the shortest range with both of these is 40 meters, and I've never been hit with a fragment at this range. Even so, eye protection is still mandatory.