Nothing risky about it.
Any member of that counsel knows that without the US, every member is a deal lump of flesh the moment we leave. We don't have to keep any special deals. You can predict that most people will make decisions that keep their asses from being blown up. They wont be going off the reservation. They can pull strings with no fear of dying as long as the US has a reason to protect them.
Zackly, and well explained. We may not own em, but they (future Iraqi govt) will damn sure know who they need to kiss up to!