They could get a marriage license from any clerk of court.
As far as I know only one of the couples even lived in Rowan County.
They came to her because they knew she was not issuing license to anyone.
Even though most of them didn't even live in Rowan County or even in Kentucky.
Typically if you want to be married in a particular jurisdiction, you have to get a license from that jurisdiction.
Jefferson Parish does not issue marriage licenses for weddings that occur in Orleans Parish.
I cannot speak as to Kentucky law but I would suspect it is the same.