No, it's more along that the lines that they claim marriage is exclusive to their religion.
Wait, what? They think that people married by other religions' methods aren't actually married?
Bizarre, isn't it? I don't quite get the justification, but I have the distinct impression that they view marriage a religious sacrament. Perhaps they recognize people getting married under other religions, but if you're a blaspheming gay, no way.
My argument is, if marriage is a religious right -- and I think it is -- then the U.S government has no authority to restrict it. In fact, I don't think 'marriage' should be part of the legal lexicon at all. It should be replaced in entirety under law with civil unions. You wanna get married? Fine, any church that accepts you can do it. You want a civil union and all of the legal rights & obligations that go with that? Talk to the gov. I think part of the problem is that the government is intertwined with marriage now, and they need to be taken out of the equation.
Honestly, I think it's just a matter of time before laws that prohibit gay marriage in the U.S. are struck down as unconstitutional.