This is ridiculous. A justice of the peace doesn’t have that kind of discretion, and the reasoning is just silly.
I'm not so sure that's correct. A JP must issue a marriage license but I don't think they must officiate.
And despite the wording of the article, my understanding is that the JP simply refused to sign the marriage license (something that can be done by a JP, any other judge, ministers, etc.). I'm not certain anyone has an obligation to officiate your wedding.
This doesn't mean he's not an idiot. I just don't think he's legally wrong.