And where would they store this oil anyway? It's rather dangerous to store, and it's pretty difficult to hide the facilities. Back in the 1970's when there were price controls and long lines, many consumers would hoard fuel, increasing its scarcity. High prices are a disincentive to hoard.
In the ground back at the well, in oil tankers floating around the world (they are cheap in comparison to the value of the oil carried), and in oil storage farms around the world that are not well reported or regulated at all.