Replicated your problem. This is what I did. Since you said you were
editing the page in designer, I did the same thing. Created a flat view
with no folders, and then when I went into SPD and converted it to XSLT,
the files disappeared and only folders showed.
When you're in your data view in SPD, and you have the Data Source
Details pane showing on the right, you'll see "Current Data Source" at
the top of that toolpane, and a link to open the details about that
current data source. Open that link.
There's a drop-down box that says "Item and folder scope". Change it to
RECURSIVE.
After that, you'll notice that the "name" field in your table will be
empty. For your data view, click to "Edit columns", and add the "Name
(for use in forms)" column.