Also not true... It was landmark U.S. Supreme Court precedent Reynolds v. United States in 1878 that made separation of church and state a dubiously legitimate point of case law, but more importantly; it confirmed the Constitutionality in statutory regulation of marriage practices...
I know that the Supreme Court has said that in the past, but that doesn't make it the "correct" decision. It may be the law of the land for the time being, but that doesn't make it what the Constitution says.
The concept of precedent is fairly incompatible with a written constitution. Precedents are a system that are more suited for situations that involve common law so that you have something to go on, but when you have a statutory text to go on you should stick with the source when you make a decision.