Directly from the links you posted:

- Halfaya: CNPC, Total SA, Petronas

- West Qurna: ExxonMobil, Shell, Lukoil, Statoil, Eni SpA, CNPC, Petronas

- Rumalia: BP, CNPC

- Majnoon: Shell, Petronas

Of all these, only ExxonMobil is an American company. Shell and BP are not American, regardless of the presence, unless you want to call Exxon a British or a Dutch company as well.

But more importantly, all these contracts were awarded on a competitive basis, with a bidding process. Especially telling is an entry for Rumalia field: "ExxonMobil which also bid on servicing this field at a price $4.80 walked away due to price cutting terms by the Iraqi Government leaving BP and CNPC as winners of the contract.".