I think a lot of this analysis is tautological -- meaning that when you boil it down, you're just saying that things are as you have defined them to be.
For instance, take a Big Five trait such as agreeableness. How do we know that a person is agreeable? Because we define agreeableness in a certain way and then measure the degree to which someone conforms to the definition. If that measurement includes questions such as, "Do others find you easy to get along with?" then of course there's going to be a negative correlation with loneliness, because you've essentially defined it that way.
I am the author of Correlated.org, which commits many different types of statistical errors for humor's sake, so this leaps out at me. By the way, for a surprisingly vast number of things, agreeableness is quite predictive. Food preferences, public policy positions, and even willingness to answer poll questions :)