First, let’s try fetching the image.
$ curl -A Twitterbot "http://invocation.co/modules/Repository/Resources/vendor/thumbnail/generate.php\?src\=https%3A%2F%2Fimg.youtube.com%2Fvi%2FtiVL3hIoMgE%2Fhqdefault.jpg\&w\=1920\&h\=960\&bg\=000000\&f\=png\&zc\=T\&hash\=fbdc96e4e4606c41554a84487d66cf70"
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML 2.0//EN">
<html><head>
<title>403 Forbidden</title>
</head><body>
<h1>Forbidden</h1>
<p>You don't have permission to access /modules/Repository/Resources/vendor/thumbnail/generate.php\
on this server.<br />
</p>
</body></html>
Now, let’s check why that might be denied.
$ curl http://invocation.co/robots.txt
User-agent: *
Disallow: /app
Disallow: /config
Disallow: /docs
Disallow: /images
Disallow: /install
Disallow: /javascript
Disallow: /lib
Disallow: /locale
Disallow: /modules <--- This prevents ALL user-agents from accessing your image.
Disallow: /plugins
Disallow: /system
Disallow: /themes
Disallow: /admin.php
Disallow: /ajax.php
Disallow: /jcss.php
Disallow: /mo2json.php
Disallow: /user.php
As stated in the troubleshooting post and page, your images MUST be accessible to Twitterbot (we obey Google’s robot specification). This is clearly not the case for your site. You’ll need to resolve this.