No, my chain is not "clean", just like the underside of my car, the bottom of my shoes, and the sewage pipe of my toilet are not "clean". There are some devices in the world that are not meant to be operated "clean". These devices can be kept operational with the correct maintenance, even if their operating environment is not "clean".
In the context of a bicycle, a "clean" chain is one where the lube is not carrying grit that accelerates the wear of parts, and does not contribute to a build-up of gritty sludge on those parts. It has been the observation of users, as well as the laboratory testing of ZFC, that wax lubes do a better job with those factors. If you prefer to continue to use oil-based lubes, that's fine. Have at it. Others have found that the benefits of wax lubes are preferred.