Cal, I don't definitively know the answer to your question - i.e. can any decision of a U.S. District Court be referred to a higher Court of Appeal. I am not from the US and anyway, my "super power" is in reading and deciphering legal documents. 
Having said that, in most countries in the western world, any decision of a lower court can be appealed if it can be shown there is cause for appeal -ie there has been an error by the Court in fact or in law. In which case, you can be granted "leave to appeal". But it is a high bar, not a right. I assume the same applies in the US.
Others may know more than I do.