I was addressing the law too. A habeas corpus petition can raise any manner of rationale for release. I haven’t found the appeal motion. News report say it merely amends her previous argument, which makes me think that it does not raise the argument I suggested - that incarceration via contempt is fruitless from the start, and is therefore an inappropriate remedy.
Appeal Filed in Kim Davis’s Contempt Ruling
http://www.nytimes.com/interactive/2015/09/06/us/document-kim-davis-federal-appeal.html?_r=0