Actually, I might have been overstating the limitations.
The SplashScreen tiddler has to be tagged with $:/tags/RawMarkupWikified/TopBody. This means that the content of that tiddler can contain wiki syntax, including output of content filtered by matching a tag.
However, the output it produces will then be statically embedded in the HTML file to show that output the next time the file is loaded. Thus, you *can* select a randomized "factoid" to be included in the SplashScreen when you *save* the file, but you can't select a randomized factoid when the file is loaded. The randomly selected factoid will remain the same each time the file is re-loaded, and will only change each time you re-save the file.
-e