"Even if we take the ground, we do not share the culture," she said, "and in the end we have to learn to coexist in a world with religious states that we may not agree with and find ways to cooperate."

This lady is definitely confused. First perhaps she is simply confusing Iran with Iraq- her POV might make some sense if that was the case.
As to the first part of her statement. We aren't "taking ground". We use ground troops to "take ground", but that's not to say as a nation we are acquiring real estate. We will have miltary rule after Saddam leaves, that's to stop riots, looting, and civilian mob justice; AND to prevent countries in the region from involving themselves in a disintegrating State- or even solely locally run insurrections.

Another thing is we CERTAINLY won't be trying change anyone's religious beliefs- we aren't having any problem currently with "coexisting" with different religious states.
Religion isn't the problem. Things like terrorism, tyranny, and torture are problems- it doesn't matter what kind of religion is used to justify it.