My point is that I am quite sure that that is NOT the standard where denial moots the case and a life is involved. I would bet the farm on it. It is more in the nature of a balancing test.
Unfortunately that is not the case, the judge must balance the competing harms of action versus inaction to each side, and he must find a likelihood that the parents will ultimately prevail on the merits. that doesn't mean they do ultimately appeal, just that it appears likely at first blush. You can well imagine that a judge can "play" with these concepts as he chooses. I could word a short order ruling either way in about ten minutes each. But there is no way around the requirement for issuing a TRO, it's in the Federal Rules of Civil Procedure which govern the court's issuance of such an order.