We're only energy independent in the sense that we export more oil than we import. We're still reliant on foreign oil because we haven't retooled (or built enough new) refineries for a lot of the oil we produce. Allowing the Saudis to own refineries is probably a strong factor there. If the middle east and Canada cut us off, we're SOL. Venezuela barely produces anything right now.
Retooling refineries to a different flavor of crude is expensive, but not that expensive. If push came to shove, the US could transition to oil independence in less than a year.