Hi
I would err on the side of caution and secure it with proper straps. You cannot afford to take the chance. A 650 litre tank weighs about 650kgs +. In an accident I wouldn't like to then find out that those securing eyes weren't man enough for the job. Remember, the tank is usually situated very close to the back of your seat.
I would strap them down properly though the floor with decent flat plates underneath to ensure that any stress is distributed.