From what I can tell, our forum software uses a custom Plugin for TinyMCE - Its called: 'imageupload.js'
The standard Image Loader, allows you to paste a Url into the Source Field.
The image is loaded into the TinyMCE Editor, but the source for the image is the Url provided, the Image is not uploaded to our forum.
The Custom Plugin does a good job when it works, it grabs the Image, uploads it to our Forum, gives it a name and directory and provides a new Url to TinyMCE Editor so it can be displayed.
I will keep looking into it, it does appear some computers are not loading the plugin, or the plugin is failing to load.
FYI: The Text version of the plugin is attached below.