That would be normal - the plane's insurance usually covers liability for injuries etc. You will need to check with the person you hire the plane from....
If that isn't covered on the policy, then a call to one of the two biggies can get you a non-ownership policy which covers you (and passengers) on any aircraft you're authorised to fly.
As an aside, are you saying that you hire aircraft with no idea what the insurances of the owner are? Or at least what your liabilites would be? What happens if you crash with a plane full of mates, injure one and they sue you?
UTR.