I'm not sure what else there is to say, I think you are assuming the Humax stuff is implemented the same way as a PC or something.
The (HDR-FOX) DLNA server is a blob of code within the Humax binary which receives DLNA media content requests and responds to them from its internal database. To construct that database it periodically (and particularly during the shutdown housekeeping) walks the Media folder tree looking for media files and adding them to the database. The equivalent of an "XML file" is the SQLite database (but I've already told you that). VLC composes the media list it presents to the user locally, from the responses to queries it gets from the DLNA server and however VLC wishes to present that information – it is irrelevant how the information is created, you don't get to see the source.
If the intention is that you want to grab the entire index, there is nothing to stop you compiling DLNA queries yourself and capturing the responses, but I guess you will have to parse the responses to request the deeper layers of the media tree. You might even find downloadable tools to help you do just that (eg UPnP Inspector). Bear in mind that the numeric .TS is assigned by the DLNA server when it walks the tree indexing media files, and does not exist anywhere else.