I don't know about no car. I had a car from 1987, namely a Ford Escort, that was incredible good on fuel. 40MPG on a trip was not uncommon and at least 30 MPG local driving was the norm.
A large SUV is of course quite lousy on fuel, but fully loaded with family, luggage and a rack with 4 bikes is an impossible task for the Escort. Plus if there is a creek to be crossed, the Escort would have to float it.