Seems to me the fact that you're considering this is evidence to say there must have been something good in the relationship although they did hurt you. If they were never important to you in the first place it wouldn't matter and you'd easily just move on. that's something to consider.

so with that said, they sound like they are sincere. Look at it this way not only are they apologetic, in any relationship whether it is rekindled or a new one you take the risk of them hurting you... either for the first time or again. it doesn't matter because you can't know the future. What is factual is that they are not above reproach at this time and asking your forgiveness. Isn't that what friendship is about in the first place? Being able to accept that we are all flawed, do stupid things and may even, god forbid, hurt each other. A strong friendship does not mean one where each does not ever hurt the other but that there is a strong enough bond that we can admit our mistakes and the other can forgive.
No guarantees she won't hurt you again. If it was all guaranteed and we knew the outcome of everything whether it be relationships and otherwise, does it really hold much value? Trust isn't something that means you're guaranteed nothing bad will happen, it means you believe in the person you trust that their word is true.

If you're telling yourself you can never trust them if there's a chance they can do it again, you might as well go inside close the door and never interact with another soul again...