How does WP Stagecoach use hotlinking?
To make staging site creation more reliable and faster, by default WP Stagecoach does not copy you media files (images, movies, etc) from your live site to your staging site, but instead, the staging server checks for a local copy of a media file, and if it doesn’t find it, it hotlinks it from your live site, so they staging site should look identical to your live site.
If your live site lives on your localhost, the hotlinked images will not appear on your staging site because they are not available on the internet.
If your live site blocks hotlinking, you will need to add an exception for wpstagecoach.com for your staging site to work properly.
Also see Images missing on staging site