Can You Export Entire Tree as Directory Structure?
 

When I export a tree, it seems as though it will only export as a flat directory of files with an XML file that represents the tree structure.

Is this true, or is there some way to export the tree so that I have a directory structure that matches the UR database?

Choose the 'Documents and item rich text to a folder' export option, and check Export child items (recursive). This will create folders/items for all the selected items and all children (except leaf text items that have no text).