One easy step they could take would be to simply say, on their website, "This site considers itself to be part of the Wikimedia Movement". (alternate text welcome )
That would be a trademark violation. We should protect our trademarks. We don't want them associated with just any project. The Foundation, or its delegate, needs to approve any affiliations. Letting anyone call themselves part of the movement could cause us significant harm since an affiliation doesn't just say that the project supports us, but that we support the project. We don't want people claiming we support them unless we actually do.
Precisely. So what do we want them saying instead when they're in that situation? We can write the text, we can design the badges, we just need to let them know what we want that text and badge to be. And, of course, we need to have it reflect something ABOUT them that they would put it up-- it can't just be a link or a banner, it needs to be about movement identity.