Ok, this is really weird now, because even my Windows PCs won't access the files. I get the error: "The remote media library did not allow the connection. Please contact the device manufacturer for more information", when I try to connect from Windows Media Player.
This used to work, before I had to do firmware upgrades, factory resets, swapping for a different device etc... which makes me wonder if something has changed in a more recent firmware, that has broken this function.