That's your original quote.
The grid is not our storage capacity.
The grid has storage capacity available to it and is the energy distribution network; the storage is connected to the grid.
Similarly, the grid itself isn't the nation's generating capacity; most generators (I'm sure your know that not all of them are) are hooked up to the grid.
At present, it probably has the majority of the nation's storage capacity connected to it (in the form of pumped water, presumably measured in GWh, not GW).
I can't put power into the grid for storage; that storage isn't storage for the nation in general but only for the generator that has direct access to it; they can put power from it - typically by running stored water through the dam turbines - and then put it on the grid.
When large battery storage is available (like in Oz), they'll be able to consume excess power from the grid and store it, but it's still not available for the nation in general but is just another power consumer and producer, connected to "the grid".
