Techdirt is reporting that Against Monopoly is reporting that HBO is sending take down notices to people who have uploaded their own recordings of the Inaugural Concert: We Are One. I haven't been able to verify this, but if it is indeed the case, it would seem that HBO is misunderstanding their rights under copyright law. Note that I am not a lawyer, so this is not legal advice.
Since HBO merely owns the copyright to their recording of the concert, they can't control what other people were doing with their own recordings from their own cameras. This is because a work is not entitled to copyright protection unless it is fixed. The actual performance that happened that evening wasn't fixed or copyrighted until it ended up on HBO's tapes (or hard drives).
If the content of the concert was in the public domain or free (e.g., The Star-Spangled Banner is in the public domain since it was created prior to 1923), then any audience member who recorded it had the right to make a recording of it and distribute that recording since they owned the copyright to the video. Putting aside questions of anti-bootlegging laws (which are arguably unconstitutional and not relevant to DMCA takedown notices), it is not clear that HBO can prevent distributions of privately filmed performances of public domain works that were performed in a public venue, which, if the Against Monopoly report is correct, is what part of what they're trying to do.
However, according to the Wikipedia page, a lot of non-public-domain non-free content was performed.
Which means that by recording and distributing a live performance of say, a Bruce Springsting song, an audience member might be infringing on the boss' copyright, but probably not HBO's copyright. Does anyone know more about bootlegging laws and how they might or might not apply here?
So what right does HBO have to send takedown notices for other people's works? Sending fraudelent DMCA takedown notices is itself a violation of the DMCA, so if you've been threatened by HBO for posting videos you recorded at the inaugural concert, you probably have the right to file a putback, and perhaps take action against HBO.
There are bigger questions, however, about the inaugural committee's right to leverage tax payer money and support to sell off exclusive rights of a public event to a private entity such as HBO. I'm not clear on whether their status as a legal entity would entitle them to do this.
Anyway, while I would like to see HBO put the concert into the public domain along with other works of the federal government, that is probably impossible as the recording contains works that are in copyright, such as Bruce Springsting songs.
There is the possibility that HBO could put the video but not the audio into the public domain, but I do not think there is an easy work around for including both the audio and video. This is not to say, however, that HBO is justified in sending nasty letters to citizens interested in helping celebrate an important event.
I sympathize with the inaugural committee's desire to produce and execute a fantastic recording of a historic moment in American history. I know that this kind of production costs money and there must be incentives for creating it. But I think the conflicts between HBO and citizens indicate that copyright is not the proper incentive here. It alienates too many citizens interested in documenting their own version of history, and given the context and content of our current president's administration, sets the wrong precedent for sharing that history. HBO should be ashamed of themselves.