This answer talks about a "closed basin" that has an outflow to the sea.
I had previously assumed that "closed basin" meant the same as "endorheic basin", but that is obviously not the case. What is a "closed basin" in this context?
An endorheic basin refers to the surface-water flow. The Great Artesian Basin refers to the groundwater aquifer (the artesian part of the name), not the the Lake Eyre surface water basin, which is endorheic. Part of the land area above the GAB is closed with respect to surface water flow. Endorheic basins may or may not be closed with respect to groundwater. In fact they may be closed with respect to water in local groundwater flow systems but open with respect to deeper flow systems.
It is common for endorheic basins to be open to groundwater flow. This can occur in a number of ways. The groundwater flow may only be affected by recharge within the basin and not discharge to surface water bodies within the basin. In the case of confined aquifers, it may be essentially separate and unaffected by the surface water or shallower groundwater in the basin but may flow under the basin and exit the other side. Groundwater can discharge to flow-through lakes. These lakes receive groundwater discharge on one side but recharge the groundwater downgradient.
He didn't say the Great Artesian Basin was a closed basin. What he said was that in the north there was some run off into the Gulf of Carpentaria, but everywhere else the aquifer behaves AS THOUGH it were a closed basin. For it to be an actual closed basin it would need an impervious perimeter which prevented drainage into the Gulf of Carpentaria.