Even though Red has blantantly lied at this point, he is Keen's father. The burn scars show us that. So I am sure he will say something about how he didnt't lie because he changed that day and was no longer her father. My guess is the fire wasn't an accident.
Therefore, with the mother already dead Red realizes he can no longer protect his daughter. He takes her to his friend Sam and he raises her.
Berlin carries a picture of his daughter and is seeking revenge for her. Red has a picture at the end of the same girl I do believe Why would he have her picture and Berlin be after him? Berlin's daughter was Keen's mother/Red's wife.
They said what got her into trouble in the first place was falling in love with someone. That someone was Red. This explains why Berlin is after him and why he is so protective of Keen.
I think this covers all bases and is probably already listed somewhere else but let me know what you think.
