Aside from what Rosseau claims, this would seem to be the most likely story:
Danielle arrives on the Island in 1988 as part of the Dharma Initiative. She manages to survive the Purge, does not convert to the Others, and flees to live in the jungle. Just as Kelvin and Radzinsky survived the Purge by living in solitude, so does she. Her story of having to kill the other members of her team? They converted to the Others and she fought them to escape, but they kept her daughter. Over the intervening 16 years of solitude she goes insane and her delusions of her past become reality to her.
Danielle arrives on the Island in 1988 as part of the Dharma Initiative. She manages to survive the Purge, does not convert to the Others, and flees to live in the jungle. Just as Kelvin and Radzinsky survived the Purge by living in solitude, so does she. Her story of having to kill the other members of her team? They converted to the Others and she fought them to escape, but they kept her daughter. Over the intervening 16 years of solitude she goes insane and her delusions of her past become reality to her.