You have the power calculation right. 9W of dissipation means that the regulator must be bolted to about 100 square inches of aluminum...
Minor nit: any three legged regulator obeys Kirchoff's Current law:
the Σ of currents in the three legs = 0
So technically, if the load draws 3A from the output pin, the current into the input pin is the sum of the output current and the current that flows out the ADJ pin. Also, since it is an adjustable regulator, there are two resistors to set the output voltage. There is some additional current that flows from the output pin down the voltage divider.