In The Devil's Arithmetic, what could Hannah have said to Commandant Breuer when Reuven is sent to his death (instead of saying that his mother died)?

The truth is, there is probably nothing Hannah could have said to the Commandant in order to save little Reuven. Hannah cannot help but feel guilty due to her desperate exclamation.  This makes the reader wonder what Hannah could have done.  Instead of yelling in desperation that Reuven’s mother “is dead,” perhaps Hannah could have said that the commanding officer of their barracks needed particular information about the hospital from Reuven (which is where he just came from).  She could then say that Reuven is crying because he is late in informing that officer.  The reason why I suggest this particular thing is that Nazis (and especially those with the rank of Commandant) are definitely good at obeying their superiors, no matter what.  Anything that seems to disregard the chain of command would be feared.  Hannah would have to make it look like Reuven was being used as some kind of Nazi tool at the hospital in order for Reuven to escape death.  Honestly, though, the chances of someone in Hannah's desperate situation going through that thought process, determining the right thing to say, and having the courage to say it would be a rarity.  Further, even if Hannah was successful, there would be the chance the Commandant would not listen, not care, or take the risk anyway.  The Commandant could also have simply sent Reuven and Hannah to their deaths together.