5.x adds a nifty feature to aggregate multiple CSS files into one, so that page loads happen more quickly. However, the current implementation is disabled if the file download method is set to "private".
The attached patch against 5.1 allows the feature to work in private mode, as well. It installs a new menu callback function that accepts the name of the CSS cache file to load. Care is taken to ensure that only CSS cache files can be loaded this way.