Some social media sites will restrict information that is directly harmful -- you can't create a subreddit to share methods of suicide for example -- so they may want to consider whether they've drawn the line in the right place.
If a site bans pro-anorexic content they've already said they're happy to restrict free speech if there's a strong enough protective need.
When the news covers shoots (or stories like this) they ARE trying to attract more viewer, it's a very different thing IMHO to just leaving up posts and allowing users to share. I see Tumblr taking down posts extremely disrespectful to the deceased. Let's not pretend a blogging platform is to blame, instead let's blame the real people at fault: the parents and the communities that drove these kids to what they saw as their only option.