Drupal says "The directory sites/default is not protected from modifications and poses a security risk. You must change the directory's permissions to be non-writable" when the permissions for the directory are r-xr-xr-x (555), that is, no account is allowed to write to the directory. Screenshot attached.
Paradoxically, when the site directory's permissions are changed to 755, the error goes away, and the status report says everything is fine, so Drupal thinks a directory which is writable is non-writable, and it thinks that a directory which is non-writable is writable.
chmod 555 sites/default
Modify Drupal so that it can correctly detect the file system permissions for the site directory.
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File system permissions detection now correctly recognizes when the site directory is non-writable.