Considering how she looks and, as you said, she was more or less on her own for a while it really do seem likely.

She is a normal human, hehe. :)

Well, as many people has already answered, Ayu's past was not so good.
Her parents broke up, she has been treated my her grandma not her mom, so (I think) she might felt lonely. Moreover, she has admitted many times ( for example, in AYU READY) that she doesn't like school and spent most of her teenage time on working and traveling. She even used to work at roppongi as a dancer at night when she hasn't reached 20 years old yet.

But one more topic,I would like to bring to this forum is the word that everyone has translated into forgiving, maybe,doesn't really mean forgiving.

For example,...
RAINBOW:
"I was forgiven by forgiving many things ..."
"yurusu koto de yurusareteta"

CAROLS:
"that i can forgive my past someday...."

"Itsuka kako wo yuruseru hi ga
Kuru to ..."

Even I am not the Japanese Expert, but from learning from the dictionary and asked my Japanese friend and Professor,
those words "yurusu" , "yuruseru"and "yurusareteta" ,sometimes,can be translated into "acception" ''can accept" and "was accepted", as well.
So I think, maybe, she is just waiting for the day that she would really be able accepted herself,both past and present. Just like many people that don't want to let the others know about their dark past. Many people try to hide their past, shy to tell about thier imperfect past and so on.
And I am wishing her for that day to come.

That's a good point, but I think that's the thing with many Japanese expressions, they balance somewhere between the meaning of equivalent words that other languages have... After all, you could say that "forgiving" is in fact "accepting" someone or something - despite what the person has done or what things have been like to us...
Although "forigiving" in fact seems like a wider expression than "accepting", so it would be nice to know if it's really this or the other.