That was a poorly written article. It left out a key fact: the school offered to let her wear a badge WITHOUT the RFID tag. Her parents still objected that this violated the word of God, and would condemn the family to Hell if they complied.
The fact that all the attention has moved from the original privacy concerns to simply a religious debate, I think, is very telling of why they lost the case.
Perhaps they thought a religious angle would fair better since religion gets a pretty wide blanket of protection these days as we are all forced to tread lightly when talking about other people's religious freedoms. But the risk in that is people seeing them as nut-jobs. The "mark of the beast" argument was really, really stretching things so it makes sense that they lost. Privacy might have been a issue, but even that is pretty weak.
