I have blithely and overcynically said for years that "the news always gets it wrong, as one can verify whenever it reports something you have first-hand knowledge of." After which, I immediately believe the next article, of course. That's what readers do. They believe text.
I fell into that with the Kim Davis story. I accepted the CW that she was attempting to deny any gay couple who came in the door a marriage license. The truth is a little trickier. She's objecting more narrowly to having her name on the forms. She says that she would be content with "Modifying the prescribed Kentucky marriage license form to remove the multiple references to Davis’ name, and thus to remove the personal nature of the authorization that Davis must provide on the current form." (Exact quote) It's not very different from the antiwar "Not In Our Name" petition against invading Iraq. Both her supporters and her opponents seem to be missing the point.
It's possible to still disagree with that. In fact, I think both the Kim Davis and the "Not In Our Name" arguments are specious. But I at least see the point, and it may fit the law. As is often the case, the Volokh Conspiracy provides an interesting, balanced analysis.