Vintage Airstreams also had air pressurized water cylinders fitted with Schrader valves. Early tanks were galvanized steel; later versions were aluminum. The trailer industry began using 12v demand pumps rather than air pressurized systems in the early 1960's.
Example of Airstream tank:
Air pressurized tank from Streamline trailer:
I think LuckyDan is correct that one cannot pressurize a poly tank with air - it would bulge and increase volume rather than build pressure, and most likely leak long before working pressure is reached.
I use a simple gravity feed system with the 13 gal. poly tank in my Bantam trailer (ignore the rust on the "radiator" fill tube - it was wirebrushed off and painted after the photo was taken).
If I ever find that I "need" running water I will plumb an inexpensive RV hand pump faucet into the system and call it a day.