Do you or have you ever lived in New York? (I have - that’s why this ticks me off so much)
Her supervisors stabbed her in the back. The policy, if applied uniformly, fits easily within the boundaries of the law. The lesbian pair demanded an exception from policy, and the clerk’s supervisors appear to have not sided strongly with established policy.
She did not relegate it to another “entity”. A policy that marriage licenses are signed by appointment only and gave responsibility for fulfilling those appointments to a senior member of the clerk’s staff. The clerk herself and the clerk’s staff are (or should be) the same legal entity, as the position is not considered to be an individual, but an office.
It is also possible that the courts themselves decided they knew better, and disallowed the policy argument.
The reason for the policy is the first amendment issue. Therefore, if the policy argument falls flat, one argues the reason behind the policy.
I’m not ashamed to admit I grew up in New York State, but it’s getting close.
I sympathize with everything you said, but your quote above is the heart of the problem. If she was the only one there, who at the time, was authorized to perform this duty, then she should have, distasteful as it was.