Is there a mechanism they could use for blocking access to the file from within git without rewriting all of the commits (and therefore changing hashes)?
I'm not sure I completely understand your question, but my guess is they are blocking access to the file from github.com which is all they need to do to comply with the DMCA request. They can't do anything about people's local copies.
Sure, they can block access to the file from their web interface. I'm asking how they block access to a specific file when someone does a "git clone" or "git pull".
It sounds like they just wait 24 hours to get contact.
"because GitHub cannot disable access to specific files within a repository, we will contact the user who created the repository and give them approximately 24 hours to delete or modify the content specified in the notice. We'll notify the copyright owner if and when we give the user a chance to make changes."
