Adding and changing things does not necessarily precipitate passing off the work as one's own. I could be wrong, but I don't think there's a big problem with that with the truly free licenses like MIT...so I'm wondering - what's the point?
Node.js has been super popular for the past few years and it's built from mostly MIT style licenses. It's so hot that Microsoft has made a big effort to make it usable and provide tools to work with it on Windows. Nobody that I know of has come along and taken this product, re-branded it and then pawned it as their own creation.
I understand that the point of the Affero license is to prevent "Tivoization" of a product, but it seems to come at the cost of not being able to attract a large base of developers to contribute to the project, since everyone would rather be working with more liberal licenses.