I think you'll find that a passenger is covered by third party insurance for the aircraft. What you may need to check is whether you are covered for any damage to yourself.
On one of the aircraft I fly, the pilot is specifically excluded and needs separate personal insurance to cover any loss of earnings/injury etc resulting from an accident.
It's best to check before you hire to find out the terms and conditions, and also what excess applies. A group I used to belong to had an excess of £500.
A group I belong to now has a "Prang Club' policy, where for £30 a year the excess is waived unless you have a fuel related accident (ie running out while in the air).
RD