One of my favorite expressions is "You can't guard against the arbitrary." No matter how well-prepared, how carefully planned, or how rigorously considered, stuff happens. The flight is delayed, the power goes out, the hard drive crashes, the road is under construction, a person does something impossibly dumb. I believe those of us who work with technology may know how arbitrary life can be better than most.
No school will ever be able to keep students completely safe, either physically or online. Kids will fall off playground equipment and get hurt. Somebody will bring a balloon to a classroom that has a child with a latex allergy. Students will get into inappropriate websites. Kids will use social networks to bully others.
What mitigates liability that schools have in such cases is if they can show "due diligence" in working to prevent such occurrences. A school should be able to demonstrate that it has chosen playground equipment with a good safety rating and maintains it regularly and that it posts "No Latex signs at building entrances.
Due diligence also means that schools do their damnedest to teach kids to be safe and appropriate online. It means having an articulated curriculum that is taught to every child. I would add that an assessment of understanding of safe and appropriate use should also be considered due dilegence.
And no, over filtering cannot be considered due diligence.