A media server does have its own menu structures / folders and will organise files by type more predictably than the Live.
The problem (and I’m happy to be corrected) seems to be that the OP’s parents don’t like having to navigate through the various menus to get to the point of actually viewing the network share / media server. The OP has already simplified his network shares to the point where it sounds like he’s acted as his own media server (videos are in a separate video share?).
My experience with TVersity is that when you select it as a media server you’re then presented with a number of potential folders to open, which can be confusing. The only way to change the default menus / visible folders is to mess with the default XML files and create a custom config (something I’ve yet to wrap my head around). If I’m mistaken or there’s a guide for dummies out there, someone let me know!
Other media servers may offer a simpler view of your media, so it’s worth looking into in that regard (there’s PS3 media server and PlayOn for starters).
However, that doesn’t change the Live’s menu structure, which doesn’t let you jump to a default share folder after selecting ‘Video’. It’s the extra clicks after selecting Video that seem to be the issue, not the OP’s network shares or media organisation.