It is actually quite simple to combat this, technically. Embed an (invisible) watermark into the video that encodes the domain for which the movie can be played, and have all browsers refuse to play content with watermarks that are of a different domain than the one shown in the url bar (throw a security exception or something).
Using the example in the article, we're already dealing with companies that are willfully violating copyright (not some dummy kid uploading tv clips to youtube with "no copyright entended" in the description).
How do they not also work around this system?
Say I go on youtube, download Destin's video, cut out his talking and advertizing portions. I'll just change the watermark while I'm there and then slap it on facebook.
Even if we go cryptographic, and replace the watermarks with public key signing, does facebook only host properly signed videos? Then how does the chain of trust work? For automated transcoding by youtube and the like work? How do I get a trusted public key for cute videos of my cats that doesn't create an infinite well of keys for freebooters?
So maybe we can't just sign, we have to add in DRM so that only authorized player widgets can even decode the video in the first place. That doesn't stop piracy of hollywood material, why would it stop a media company from freebooting?