Liar or Not?

The only things we know about Rousseau and her history are the
things she's told us about herself. Do you believe her story? And
while you're thinking about her -- did she arrive on the Island
before or after the Purge?
Sayid: And how did you come to be on this island, Danielle?
Danielle: We were part of a science team.
Sayid: A science team armed with rifles? Was Robert on the team?
Danielle: Yes.
Sayid: And Alex, was he, too?
Danielle: Our vessel was 3 days out of Tahiti when our instruments malfunctioned. It was night, a storm, the sounds. The ship slammed into rocks, ran aground, the hull breached beyond repair. So, we made camp. Dug out this temporary shelter. Temporary. Nearly 2 months we survived here, 2 months before...
Sayid: Your distress signal? The message I heard, you said, "It killed them all."
Danielle: We were coming back from the Black Rock. It was them. They were the carriers.
Sayid: Who were the carriers?
Danielle: The others.
Sayid: What others? What is the Black Rock? Have you seen other people on this island?
Danielle: No, but I hear them. Out there in the jungle. They whisper. Oh. You think I'm insane. From Solitary
Danielle: The firing pin has been removed. Robert didn't notice it was missing either when I shot him.
Sayid: But you loved him.
Danielle: He was sick.
Sayid: Sick?
Danielle: It took them, one after the other. I had no choice. They were already lost.
Sayid: You killed them.
Danielle: What would have happened if we were rescued? I couldn't let that happen. I won't.
From Solitary
Hurley: Look, I came here to find... oh, easy, easy, easy. I'm... Im just getting your notes. Please, tell me why you wrote this. What do these numbers mean? Please.
Danielle: I don't know.
Hurley: What? You don't know? Okay, that thing in the woods, maybe it's a monster, maybe it's a pissed off giraffe, I don't know. The fact that no one is even looking for us, yeah, that's weird, but I just go along with it because I'm along for the ride, good old fun time Hurley. Well guess what? Now, I want some friggin' answers.
Danielle: Our ship picked up a transmission, a voice repeating those numbers. We changed course to investigate. After we shipwrecked my team continued to search for the transmission source. It was weeks before we found the radio tower.
Hurley: There's a radio tower on this island?
Danielle: Yes, up by the black rock. Some of us continued to search for the meaning of those numbers while we waited for rescue, but then the sickness came. When my team was gone, I went back up to the tower and changed the transmission.
From Numbers
Danielle: The others are coming. Our ship went aground on this island 16 years ago. There were 6 of us... my team, 6. At that time I was already 7 months pregnant. I delivered the infant myself. The baby and I were together for only 1 week when I saw black smoke... a pillar of black smoke 5 kilometers inland. That night they came they came and took her... Alex. They took my baby. And now, they're coming again. They're coming for all of you.
From Exodus, Pt. 1