So the government handing is out copies, not just showing on a website, which prevents the copyright owner from profiting from their labor and investment.
It's not clear to me from skimming the page that Nautilus linked to who is handing out what, but if the government is copying videos without permission of the copyright owner, then sure, that would be the copyright owner's beef. However, the government might be taking the position that they are not making copies; rather, they are just making a video available for viewing by the public (a "fair use"), the same way they would be in their right to make available a film, such as an educational documentary, for viewing at a public library. Without knowing more, I'm just guessing.
We buy songs, but not the copyright to start printing CDs. But businesses an play records for customers.
I'm not sure the music business is relevant to what's going on here, but businesses are allowed to play records for customers by paying a license fee to the copyright owner.