However, it came with two templates pre-installed, and you have to choose one of them. They don't match my site, so of course I want my site's template to dictate the style of the module, but that's not an option.
The only solution supplied is in the description above: "If you want more control, you can simply override both the generated HTML and CSS, using MVC template overrides within your Joomla! template." If someone can explain to me what that means, please do. I also don't understand why you can't just select "None" in the module's styling options.