Because most people who declare themselves to be in an open relationship on Fb aren't in an open relationship. It's most often done just for the sake of being silly or telling everyone who your "BFF" is. The latter is more likely the closer you are to being a 16-year-old girl.

But why would that correlate with "negativity" across a subsection of people?

No, people in open relationships post fewer status updates with "happy" words. They also post fewer status updates with "unhappy" words. So, we might be lead to conclude that people in open relationships choose, for whatever reason, to expose their emotions in status updates less often than others. That doesn't particularly mean they have fewer emotions, positive or negative than anyone else.

You also see this strongly in the "widowed" category, who have dramatically less happy or unhappy postings.

Probably jealousy + lack of emotional gratification.