Why are stocks relevant at all if the US is the largest producer and a 3rd largest net exporter? It's not like there's any chance that there will be oil shortage in US.
For now, US not only exports a lot of oil, but it also imports a lot of oil, and those quantities cannot be compensated, because it is not the same quality of oil.
Thus there can exist oil shortage in US, simultaneously with exporting great quantities of oil.
Not really because to make gasoline, both sorts are necessary. When anyone in the world makes gasoline they need oil they import from the US and they don't need/can't substitute it with the kinds of oil US imports. So there cannot be a shortage. In addition, it is the US oil (lighter sorts) that are in more shortage worldwide because Gulf states produce similar ones and supply from there is choked. US imports heavy oil and it is abundant and will be even more abundant now when Venezuela's supplies will be returning online.
It gives US a bigger advantage than it sounds.
Thus there can exist oil shortage in US, simultaneously with exporting great quantities of oil.