In their motion, they argued that they needed a stay pending appeal of Walker's order because once the information was "disclosed" it could never be "un-disclosed," so they should not be required to disclose it until an appellate court had rejected their arguments. Walker disagreed with this reasoning, evidently. (I've not seen a written opinion, just the newspaper report.) One of the tests for such a stay would be that the party appealing the decision is likely to prevail on the merits. Walker expressed doubt as to this, writing that "it simply does not appear likely that the proponents will prevail on the merits of their appeal."