The United Nations has access pretty much at the will of the Iraqi government. But there has been some UN access, simply because the Iraqi government will not risk direct confrontation with the entire international community. They have allowed some people from UNHCR to go in, but they do it only on a very limited basis and under certain conditions. They've blocked the interview process. They've insisted that it take place outside Camp Ashraf at remote locations, and that's something that should not be done for security reasons, obviously.
On December 1st, 2011. See this statement in context.