I have replicated the situation and like yourself I get a blank white space. For a logged on user I get something like that shown in pic Latest01.png but if not logged in I get as shown in Latest02.png.
I expected to at least show the module title, the 'before' text and the 'after' text as in Latest01.png. If that had been the case adding in a message like "no downloads to show" or similar would be straight forward. But it shows absolutely nothing!
So it is a bit deeper than it first appears. There are two layouts for the module, 'default' which uses Tables, and 'lternative' which uses divs. Both have the same problem.
Your suggestion is a good one. Will need more investigation to solve and implement. Please note that most effort at the moment is getting to stable release state so please be patient a little longer.
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