Yes, she should have focused on the law. Her argument implies that she believes she is performing or solemnizing a marriage, when in fact she is simply issuing a license for someone else to perform that function. The argument would be a lot more relevant if she were a justice of the peace who was being coerced into solemnizing the ceremony.
Actually, the marriage licenses state that it is given under her personal authority, with her signature. That is the crux of the matter.
She’s still facilitating it.