As nobody seemed to be able to answer my question, here is how I worked around my problem:
So my goal was to paint a texture over an object, using image information from a movie clip (displayed in the background image as a camera clip).
My first approach was trying to use the clone brush in texture paint mode. The problem here is that it is only possible to use an image as the source. I was then thinking about writing a python script, that would use the viewer node to export an image (current frame in camera clip), load it into the source from the clone brush so that I could essentially paint on my object from the camera clip. But ... yea that turned out to be too complicated and too long for me to work on (would be a nice feature though). So I looked for a more reasonable and not so time consuming solution.
The thing I came up with seems pretty straight forward. Simply split up your movie into chunks and use one image per chunk. Then I could make vertex groups, unwrap them using camera projection and project the image that I want for that specific group onto the texture. I then combined the textures and smoothed the edges out, so that you wouldn't see them in the final result.
And that's it. I think the clone brush would have been a nicer solution, but this also worked fine.
Hope this helps someone out there :)