Pardon my naivety in such issues, but isn’t the Secret Service armed? If so, then I think that the SS would secure the school if they heard shots being fired at the school, regardless if there was no immediate danger to Obama’s daughters.
I highly doubt that would be their orders. Their orders are likely to protect the girls at any and all costs. And that does not include hunting down an active shooter unless he is the room with the girls.
Their job would be to GTFO and protect the girls only.
Can you imagine the negative PR that both the WH and the SS would get if this was the case and other students / teachers / staff got harmed? Hopefully, the SS has done some careful planning and has enough personnel at the school to handle such contingencies.
By the way, I agree with your signature line.