adult child at home (Florida)

Hi. Semi-complicated question

• If an adult child lives with at their parents' home, I understand that the child needs to be on the parents' policy if the parents own the vehicles

• If that adult child rents a car, I understand that the parents' car insurance covers them

What if the child is in an accident while renting?

I would assume that the insurance policy covers their liability. I would further assume that the parents have no further potential liability (other than their insurance costs may go up in the future).

Is this correct?

TIA.