While I think you’re probably right we don’t have a great effect on world prices, we do have a great effect on world demand and the income of foreign producers. When we consume less foreign oil, they get less money.
Obama was known for banning much oil drilling and absurdly impeding the Dakota Pipeline. His legacy on energy is mixed at best. I would credit his general inaction on fracking, which led to where we are now but that’s not to say he helped it.
The problem with the M.A. was that it didn’t have an international hook. Sanctions re Crimea (which we also have) do have that hook.