Not to belabor this point, which is of course extremely minor, but the Supreme Court did do away with the agreement factor in certain situations...imagine you live with a girl and you tell everyone that you're married. Let's say that you also mingle some assets. Furthermore, you and that girl have never agreed in any way to be married. According to the Russell doctrine, a court should find that you have a common law marriage.
Maybe the best way to explain this is to say that those factors, taken together, are sufficient conditions and not necessary ones. So a written agreement by itself can do it, or cohabitiation and public representation by themselves can do it. What's wrong is to say that all three of those factors must be there in order to prove up a common law marriage. Trust me on this one, I've proved up common law marriages without any kind of agreement before, and haven't been overturned on appeal (at least not yet!)