Iraq and Iran: Why Can't They Be Friends?

Today something happened that blew my mind. The freely elected Prime Minister of Iraq met with the president of Iran today. At that meeting, Iran's president said, "the Islamic republic supports a united Iraq and will help the nation establish full security." It blew my mind because this proves a couple of things and its the best thing the US could hope for in Iraq.
First, this should show that the current Iraqi government is not the puppet of the United States. If that were the case, this meeting would never have occurred. Everyone in the world is fully aware of this administrations hatred for Iran. Everyone is also aware that we have NO diplomatic relations with Iran. So if we were controlling Iraq's government, we would never let the PM visit Iran.
Second, this meeting shows me that it is possible to not be in the Middle-East forever. Although the paranoid would say Iran is just playing nice, what if the country is really serious. I mean have we stopped to think that maybe they are telling the truth? Have we stopped to think that maybe they don't have nuclear weapons? Of course not. We always think the worst because this is obviously a crazy Islamic state bent on the destruction of America.
If you ask me, this is our ticket out of Iraq. The Iranian president said today, "Iran will provide assistance to the Iraqi government to establish full security. We believe strengthening the Iraqi government is tantamount to promoting security, peace and friendship in that country." Good deal then. Let them work together and have the Iranians train Iraqi military and security officials. Why do we have to do it?
I am pretty sure that our government will speak out against this arrangement. But, what right do we have to tell a freely elected government who to be friends with? In fact, I don't believe we have any say in what is decided through this meeting. If the Iraqi PM came out tomorrow and said that all future training of Iraqi forces will be done by Iran, I'd skip for joy. And everyone in America should too. Our troops could come home. It would no longer be our concern. Why can't they be friends if they want to be? It is not our place to tell them.