Reddit is no different than anything else here in America. If you want to post pictures stolen from phones? Totally OK[1], unless the people in those pictures have money and thus lawyers. When the lawyers show up, Reddit will happily pull any material pertaining to the people with money, and leave everything else as it was.
What you are saying is people with a voice can defend themselves which bothers those that want to do whatever they want, but dis-empowered people, too bad so sad.
I really don't get why anyone thinks this whole event is even remotely okay, they should have banned it from day one, the pictures were obtained illegally and definitely not posted with permission, and yes they should apply that rule to all of Reddit.
Reddit doesn't owe anyone imaginary "free speech" rights, they aren't a government entity but a privately held company.
No please, don't turn this into a "people with power" can do anything rant. Reddit removed the sub because they were overwhelmed with DMCA notices. If the other sub you mentioned was also flooded with DMCA notices then it would get removed too.
Actually they'd just ignore it if it all came from one person. If it came from multiple people, that'd be a case of "people with power get what they want" as a collection of even ordinary people is a powerful and wealthy force on its own.
Instead of posting to /r/thefappening what if they were just posting to /r/pics or /r/aww ? You think they would shutdown a subreddit with millions of subscribers?
[1] http://www.reddit.com/r/photoplunder