Right now for the majority of people who get a DMCA, there is nothing they can do. There is no functional appeals process, there is no office in charge of handling bad DMCAs. Shy of actually going to court with a lawyer and attempting a suit, if a company files a bogus DMCA then you are boned.
That is an abortion of free speech and property rights, and the Swartz case is a perfect example of that. Most of the papers Swartz obtained were supposed to belong to the public, and yet he was sued into oblivion for DOING NOTHING ILLEGAL. He had no counterclaim short of going to full court with lawyers, something entirely out of his grasp and reach, and because he felt he had no alternatives to having his life ruined, he committed suicide.
It's not a farcical tragedy, it's a flipping shame for the human race.
edit - language
Schwartz was prosecuted by a US Attorney. If anything he is a poster boy of over reach of government.