The order of things is important; even moreso when those things are command line arguments.

After spending way too long (~30 minutes) trying to figure out why my background Blender renders were producing default cubes when that is clearly not what is in the scene, I finally looked at the console output and understood.

blender --background --python script.py myfile.blend

What this command does is tells Blender, "Load into memory as a background process and run script.py (which changes some settings and starts a render). Then load myfile.blend." Once the file is loaded, background Blender exits.

In the proper order:

blender myfile.blend --background --python script.py