It's usual for a group member to be responsible for any uninsured losses while the aircraft is in their charge. Most groups will have hull cover, possibly with a high deductible. If the aircraft has a relatively low value then it may make sense to have 3rd party and passenger only insurance, but there must be an agreement as to how losses are covered by the group.
Check out the agreement and if you don't like it and they are unwilling to change then walk away.
Having a personal hull cover would be quite unusual and relatively uneconomical. It would not be covered by a renter's insurance.