This rather interesting, but harmless paper is getting blown way out of proportion in this article. All they do is see who is returning information, and make hypothesis about the demographics of those people. Their methodology is very clearly explained in the article "using this threshold allowed us to record only the presence or absence of text entered, not the keystrokes or content."
Furthermore, and somewhat amusingly, "a summer intern conducted this work." Thus, it was mostly a summer project, researching demographics about people who started to comment and then stopped.
They put forth 7 major hypothesis:
1) posts will be censored more than comments
2) men will self-censor more than women
3) users with more opposite-sex friends will self-censor more
4) younger users will self-censor less
5) users with older friends will censor more
6) users who more frequently used audience selection tools self-censor less
7) users with more diverse friends will self-censor more
All of these are interesting questions based in a large amount of literature that they could uniquely address and answer with the data that they had. Recording whether or not users enter and then remove data is honestly relatively unimportant. Yes, websites taking user data without asking is an invasion of privacy, but I think this sort of article represents a type of knee jerk alarmism and exaggeration that can be incredibly hurtful to efforts to use data Facebook has available to answer interesting questions about human interaction. It also, furthermore, represents a purposeful misreading of the article, which is journalistically questionable.
If you want to read the article for yourself you can find it at https://www.facebook.com/publications/493601774027388/.