US government just needs to enforce laws against corporations abusing the DMCA. Samsung committed perjury by saying they hold the copyright to these videos.
Not quite. Samsung claimed they own the copyright to some work, and that this video is in violation of such copyright (for example, the videos could include a photo or text owned by Samsung). I don't think the perjury clause applies if they're just wrong about the latter.
They claimed copyright on a Grand Theft Audio screen capture video that had the grenade model substituted for a cell phone. No way you could argue you own copyright on that.