Moosetags might have it... If your pump doesn't have backflow protection on it, water from a hookup with a white hose CAN flow back through the pump into the white tank.
So first thing to try when you're not hooked up to city water is to turn on the pump and run water into the sink. If it just keeps running and running you've got a full or at least partly full tank.
I've seen other posters say that you can use the pump to boost your pressure if you're at a campsight with water that has low pressure... how this would work WITHOUT water in the white tank is a mystery to me.
So is it possible that Airstream deliberately DOESN'T have backflow protection from the pump to the white tank?
Now if you can ascertain that your tank is empty, it's likely that your filler tube is messed up. The one I sold GT1963 actually had a hole IN the pipe, and had apparently been twisted badly on installation.
Today is a gift, that's why they call it the present.