Myth is it? LOL! You veh' funny man.
http://www.halliburtonwatch.org/news/wolfowitz .html
"Wolfowitz, as Deputy Secretary of Defense, shaped and directed U.S. reconstruction efforts in Iraq. The U.S. government, through Ambassador Paul Bremer and the Coalition Provisional Authority (CPA), had direct control over the Development Fund for Iraq (DFI) - the account where Iraq's ongoing oil export revenues were deposited under the occupation. Until the CPA ceded authority, Bremer and the CPA were solely responsible for the disbursement of these funds, along with the Pentagon, particularly Wolfowitz. In December 2003, for example, Wolfowitz ordered that reconstruction money from the DFI be released only to coalition countries' corporations."
There is an absolute wealth of news stories from press of *every possible* political flavour that will support the fact that the US allowed corporations such as Halliburton (Dick Cheney's company) to take the oil contracts.