Yes, Chris Young took a nasty line-drive shot off his nose from Albert Pujols a couple of weeks ago. That's quite rare, even at the youth level. Do you know how you reduce batted-ball injuries? Leagues divided by age and skill levels, worthwhile practice, and field maintenance. You accept that you cannot prevent every injury, and also that if a player can't either block, catch, or evade nearly every line drive hit to him, he doesn't belong on the field. The youth and high school governing organizations have studied equipment behavior and laid out specs for bats to reduce bat speed and energy transfer. At the lowest levels, there are softer balls and breakaway safety bases. I've told players I've coached that if they lose a ball in the lights, move until you get it back, and if you still can't find it, cover your damned head. Better a ball drops than somebody gets hurt. This is common sense. I realize a lot of parents don't teach that anymore, but that's no reason to penalize everybody else.
People like this would have your children never leave the house without a bubble-wrap body suit. They mean well, but they carry it to a clownish extreme.