The preview animation shows the Sim being desperate for a friend, though in game the Sim feels better alone.
Nearby pets do not remove the Enjoying Solitude moodlet.
Loner Sims will say the following when put into a rather large outing group: "This is more people than I can handle...I've got to get out of here!" followed by their feelings on the group outing. This occurs even with family members (tested with an 8-member group outing where two members were loners. After a few sim-minutes, both quit the group immediately leaving it a 6-member group). Another test used 5 siblings, and was a one loner. The single loner quit the group immediately leaving it a four-member group.
Loner Sims dislike having the "Woo!" interaction from Party Animal Sims used on them.
Loner Sims with the Insane trait will never need to socialize with other Sims because not only will the Social need decrease slower because of the Loner trait, but also being an Insane Sim allows them to use the "Talk to Self" interaction to raise their Social need in addition to their Fun need.