"Otherwise you'll be the one telling the coppers "that kid just appeared out of nowhere" as the ambulance drives slowly off with its lights and sirens OFF."
Dude, Not Funny!
That's more real than you realize. Little kids can be smaller than the cars they hide behind and completely concealed by their bodies. They don't know what's out there, then suddenly jump A MERE THREE FEET in front of your car.
Physically unavoidable, and an emotional train wreck to boot. You CANNOT tell the grieving parents that you can't fight physics.
And PS. Parts of tree can drop pretty suddenly and without warning. Maybe not the while trunk, but think a very large and heavy overhead branch that picks that picks the wrong moment to drop fifteen feet in front of you on a crowded road (so no room to swerve). Yes, they CAN just drop. Frequent auto insurance claim, in fact.