In 1974, iirc, the arabs embargoed us and the price of a barrel of crude oil doubled overnight.
Refineries have to shut down periodically for maintenance and upgrades, otherwise, they have more serious problems and longer delays, usually after a fire or explosion.
There are many reasons why crude oil tanks can be full during a shortage, not the least of which have to do with refining capacity, but may include having just been filled with refinery feedstocks (offloading tankers--i do not know where you saw these tanks, whether at a port or inland), or waiting for pipeline space to be sent out.
In general, though, if it costs more to do than it will bring in in revenue, it probably won't get done. It is a business, not a charity.