Although things can look different/weird depending on how low the preview quality is set at, it has nothing to do with the quality of the rendered video.

You are correct that the Preview quality is independent of rendered quality, but....you can alter the actual quality of the rendered video to any of the same four levels. When I am rendering video that is to be slowed down, either in Vegas or in 3rd party software, I will render it in Preview quality to cut down on frame/field artifacts. Go to Render a video, and click on the Custom button. Under the Project tab is the setting Video Rendering Quality to see the four settings.