Typically, that dynamic is less beneficial to the oil producers that thrive when the market is bidding up prices. Although refineries can earn higher profit margins in an environment of low crude, producers often suffer a drop in profits.
Thinks may be different now, however, and energy giants are downplaying the strong greenback's impact on their operations. Mark Finley, BP America's general manager of global energy markets and US economics, said in an e-mail reply to a question from CNBC that "oil prices are primarily driven by oil market supply and demand fundamentals, rather than movements in the dollar—as is evident by the recent decline coming amid weak global demand and strong growth in US production."
Some analysts already see a shift underway in the traditional relationship between crude and the dollar. In a March research report, Bank of America-Merrill Lynch said with the U.S.'s growing energy independence was causing the negative correlation between the dollar and oil to ease.
"If you're producing more and more here and you're doing exporting, the strong dollar effect is reduced quite a bit," said Richard Hastings, a macro strategist at Global Hunter Securities. "You could look it as a hedge or a buffer…but it avoids the import/export currency effect that brings into focus the stronger dollar."
Although multinational oil giants ExxonMobil, Chevron and ConocoPhillips all reported flat to weaker earnings in the first quarter, all three reduced overseas production while ratcheting up exploration in domestic hotspots.
Chevron,the second-largest U.S. oil company by market value after Exxon, reported flat daily oil production in the U.S. during the first quarter–but its international wells saw a drop of 2.5 percent. Meanwhile, Exxon's U.S. oil production accounted for the majority of its product sales.
(Read more: US Oil Moves Inland, Making Storms Less Disruptive.)