This sounds more like an OGP problem relating to a social and/or SEO plugin (Yoast or All in One perhaps). Does Independent Publisher set meta tags with open graph protocol? I don't imagine it does.
If you view the source of the page (that does show the featured image in social media) you'll usually see something like the following in the header of the page:
<meta property="og:image" content="http://example.com/wp-content/uploads/photo_path.jpg">
This is the meta tag the social platform is likely pulling the image from.
It's possible that it's the case that the SEO/other plugin is automatically pulling the photo from the theme in one case but not the other. These plugins typically have settings to allow overriding the featured photo, using a default photo if one isn't specified, or not using one at all.
This sounds to me more like an issue with another plugin causing the problem and not the theme.