Being private companies, they are allowed to do as they wish. If they felt that certain items were terribly false or even posed a threat to national security or the security of certain groups, then they absolutely should have deleted them. The problem with social media and the web is that information is too easy to spread, regardless of the correctness of it. I support any company that helps to stop the spread of false reports.
By deleting pages containing information, one is harming the very institution of freedom of speech. Even if it's hate speech or whatnot, removing it is a form of censorship and only hurts the credibility of one's own website and its content. Additionally, it stands to reason that the method for deletion is determined by a select few people, which may (or may not) represent the views of the public. It's not up to a few people to decide for the masses.
No, Facebook and Reddit should not have deleted pages about the Orlando massacre. Although it is a sensitive topic people have the right to express their opinion about major events such as this. People want to discuss what happened in Orlando and Facebook and Reddit are good forums to do so.
Freedom of speech grants Americans the right to say what they please, even if it's controversial, unpleasant, or inflammatory. However, when users participate in a service such as Facebook or Reddit, they agree to that site's terms of service. Although users may say what they want, the site also has the right to decide what content it approves on its site. Uncomfortable or unwanted conversations may occur that many people disagree with. Comments that contain hate speech or illegal content should be deleted, but otherwise freedom of speech should allow users to say what they want.