You get "Module downloaded, but zip was invalid." because unfortunately loose-screws sends an empty file instead of an error when you ask it for a module that it doesn't have. The zip file is, in fact, not usable. If you find one that is, it's a different file.

NLM names the dll according to the module-version string, which is usually the name of the zip, because it makes the URL nicer, but doesn't have to be. (although if you have it set to save the zip archive, it will also name the zip according to this string, and the documentation)

If the theme asks for "dummy-1.0.1beta", it will ask all the download sites for it, and they should send back an error, but loose-screws instead says "here ya go, have this empty file!" NLM determines that it can't open the file, but it did get one, so it tells you this.

Any existing "dummy-1.0.1b.zip" file that you may have is a completely unrelated module as far as NLM is concerned.