I tend to agree with you. It seems to me that above all else, marriage is an agreement between two people. It is that simple. The particular laws that cover the jurisdiction in which the couple reside may require certain conditions be met before the state recognizes their union as an actual legal marriage, but that only has as much impact on the couple as they allow it to have on them. Of course, they might not receive all the marital benefits that the state entitles, so that could impact them and their union, but only if they desire those benefits.
Not knowing what the Bible states about marriage and the requirements for it, I obviously can't say what constitutes a biblically sanctioned marriage. But I don't believe the Bible to be infallible, nor do I believe it is a record of God's actual laws, so personally, I couldn't care less what the Bible says about marriage.
I think if two people decide to pronounce oaths to one another, and if in doing so they agree between themselves that a marriage bond has been consummated, then as an outside observer, who am I to challenge them?