Previous posters have claimed that the couples should have accepted a license issued by another clerk. But it appears that she was not allowing the others to issue any licenses.
Within her office, yes.
But the could have gone to a different county. Tourist-dependent Louisville is playing itself up as a great wedding destination for same-sex couples for instance.
They could have asked others to issue a license (although in violation of Kentucky law)
Ky. Rev. Stat. 402.050(1)(b) Marriage shall be solemnized only by ... Justices and judges of the Court of Justice, retired justices and judges of the Court of Justice except those removed for cause or convicted of a felony, county judges/executive, and such justices of the peace and fiscal court commissioners as the Governor or the county judge/executive authorizes