MacArthur gave the order, The commander who actually lead the assault on "Hooverville" (the Bonus Marcher's shanty town on the Mall ) was George Patton.
The "San Patricio's" were hung because they deserted TO THE ENEMY, those who were spared, (a few very young men ) were pretty much marked men the rest of their lives. In those days while the Army may have flogged , hung, and shot deserters the civilian world didn't much care, it did not have the stigma attached to it now. Troops were mostly Volunteers and it was seen a "unvolunteering". The San Patricio's however went beyond the pale by actually serving the enemy, and from all accounts serving them well.