Connected Media provides a way to browse, play and download web media. Don't allow it to confuse the way local media is handled. When selecting a media link, you're given the option to play, link or download. If you select download, the file becomes part of your media collection—like any other. It will be included in any view (audio, image or video) that includes it in it's Rules for file display. The [Web Media URL] is recorded, but it's only relevant as a record of the original source of the file. As you've discovered, it may not be the best attribute to use in your Rules for file display.
Something that is a little different—and useful to understand—is that when you choose to record a link rather than download, the URL is also recorded as the [Filename]. MC will treat this as any other file in the library—it may be tagged and included in any view. This is particularly useful for including streaming media (e.g., Internet Radio) in the library.