There aren't any oil-filled voids within the ocean floor. Oil and gas is contained in pourous rock, but the oil-containing rock is mostly solid. In the Deepwater Horizon case, it was also more than five kilometers below the ocean floor, so in other words very far underground.

I have heard the same speculations you refer to in the news, but I think they instead refered to the topmost portion of the well being destroyed, creating cracks in the top of the shaft of the well and allowing oil to leak in all directions. I am not a geologist, so I don't know how plausible these worries were.