Is the Iraqi Prime Minister an American puppet?

As President Bush opined on August 22, there should be no confusion on this issue:

Prime Minister Maliki is a good guy, a good man with a difficult job, and I support him. And it's not up to politicians in Washington, D.C. to say whether he will remain in his position -- that is up to the Iraqi people who now live in a democracy, and not a dictatorship.

Nearly a year and a half ago, Bush said virtually the same thing about the Prime Minister's predecessor:

The US ambassador to Iraq has told Shia leaders that the US government does not want Ibrahim Jaafari to remain prime minister, senior Shia politicians say.

Zalmay Khalilzad said President George W Bush "doesn't want, doesn't support, doesn't accept" the retention of Mr Jaafari, Rida Jawad al-Takki said.

Mr Jaafari's spokesman accused the US of trying to subvert Iraqi sovereignty.

In the past I have had my suspicions that decisions about the Iraqi leadership were being made by politicians in Washington, D.C.. But now things are much clearer.