This story implies that this family has visas. I understood that all cancelled visas were reinstated. Therefore there should be no problem for this family to enter the US as refugees provided they travel immediately. What am I missing here?

Although the timeframe here for approval and travel may sound excessive, I suggest on the basis of the experience of many Canadian parishes, that such timeframes are not unreasonable. Despite expedited program by the Canadian government to bring in 40K refugees (the proportionate equivalent of 400K to the US) on an emergency basis, many parishes here found themselves ready and waiting for similar periods.