[Windflier]

...if they can cram a hose into the hole to pump in mud, can't they instead let the oil flow up through the same hose?

You'd have to be able to clamp that hose onto the pipe in such a way that no oil escaped through the connecting point. It would be worse than having a loose garden hose connection.

[east1234]

They are pumping in the “mud” through little auxillary ports, if you will. Take a look at the diagrams, you couldn't “produce” from those ports without plugging the top, and those ports were not designed to produce.