Does this mean that someone could take down all of github by sending (fraudulent) DMCA takedown notices for every single repo (from some fake return address)?
And then it would then be incumbent on the users to fight that?
And then it would then be incumbent on the users to fight that?
That said, yes the DMCA can be abused. The check against that is the same check that exists against other kinds of fraud: it's illegal.
They're not hurt at all by popcorntime going down.