According to the state law I read, if the county clerk is not available, the county judge has the responsibility to issue marriage licenses. The statute says nothing about the deputy clerks having authority to issue licenses.
I get the distinct impression that Judge Bunning, being a Federal Judge, isn’t all that familiar with the intracacies of state and local law pertaining to how a county clerk’s office is run.
He seems to be winging it. Especially in saying that there’s a risk that the licenses are invalid and it’s up to the couples to accept that risk or not.