When you read a book that is writer in the first person. Do you believe everything the narrator tells you. Or perhaps you just say that's probably how she just decided to tel! It is how she remembers it. Especially if the narrator is looking back a long time ago maybe she remembering it differently.
I have read a number of first person stories and never really questioned if the narrator was telling the truth. An interesting question. I can think of two classics where the narrator doesn't know the truth so neither do we, the reader. "Jane Eyre" and "Rebecca." But truth will out, as they say.