Parents are generally answerable for minors
A claim arising from what a child posted, shared or did online is made against the household. Arizona law addresses parental responsibility for a minor’s conduct, and whichever way a particular case resolves, the family is the one defending it. Defense costs alone are substantial.
This falls under personal injury, where it exists
Defamation, invasion of privacy and similar claims sit under personal injury cover rather than bodily injury. That grant is included on some umbrellas, optional on others and absent from many, and it is rarely what anybody compares when choosing one.
These claims are defended, not usually paid
Most such allegations do not end in a large judgment. They do end in legal bills. An umbrella that pays defense costs, frequently outside the limit, is doing the work long before any question of damages arises.