It's not a permissions issue. The apache process is running as the file owner, and permissions are 644.
I can save ALL OTHER SETTINGS, just not the new "Additional Starting URLs" (it remains blank after pressing "save" no matter what you put in it).
Just for proof, I tested to confirm with both 0666 and 0777. Same behavior. Not a permissions issue; looks like a bug in the script itself (does it save for _you_?).