This is not true. You can travel to some places on your green card ("Resident Alien" card, which is in fact no longer green), and there is a document called a "reentry permit" that some resident aliens can use to travel to some places, but you must be a US citizen to get a US passport. (Check out, for example, http://travel.state.gov/passport/get...first_830.html.)

In fact, I am a resident alien and travel on a US passport, but that's because I have resident alien status in Canada. I am assuming that you are talking about resident aliens in the US.