After employing "1-click hardening", the media library stopped showing images, and the images on my site pages and posts only showed a broken placeholder image. I tracked this down to the "deny from all" statement in the /wp-includes/.htaccess file. Once I deleted that, the media library worked again, and images on my pages and posts also resumed working.
My installation is WordPress multisite in subfolders. The "root" WP .htaccess for this type of install calls for image URLs to be passed through /wp-includes/ms-files.php ... but since PHP was denied, things broke. At least that's my conclusion.
So: problem encountered and resolved, in case someone else runs into this.