You are right the buck stops here. At US Grant's door. He prevailed on Lincoln to stop the practice of prisoner exchanges--rightly so. The practice helped the South. Unfortunately given the Southern economy they were unable to adequately care for their prisoners.There is an expression, "the buck stops here". And if you read the report of the trial, civilian, Confederate and U.S. witnesses testified to Wirz's personal involvement in killing and torturing.
General Washington was a traitor--to the British crown. I doubt that he was under any illusion as to what the British would do if they captured him. As Benjamin Franklin said: "We must all hang together, or assuredly we shall hang separately."
Unfortunately their only options were to keep the prisoners they had and let them starve or release them to rejoin their armies and kill more Southern troops. What would you do?