I hope your letter burned so bright that the Devil had to run and hide!
I see that your feelings about your girlfriend have been influenced by the reputation your first girlfriend got from the rumors that were spread about her when you were at a long distance. It makes good emotional sense -- and emotions have a very "reasonable" logic of their own, no less respectable than other types of "reasonable" thinking -- that you don't want the girl you want to mary to drift into the same category as the box you emotionally locked your first love into when your trust was challenged repeatedly, AND you were not around each other to knock those anxious thoughts down.
Now I'll provide an intellectual explanation that may help to situate your and your girlfriend's experience in the midst of normal human nature. Emotional logic and thinking-logic are not the same. In fact Emotional Logic overpowers thinking-logic, though the vast majority of academically educated PhD psychologists don't understand that yet. Ordinary thinking logic could either agree with your girlfriend's explanation (drunk, afterwards disgusted, shamed, remorseful, trying to hide her shame and even sensing that your untested morality would make a really big deal out of it, so trying and praying to hide it), or lean toward your own workup: If she did it once & lied, then she could do it again & lie again, just like the first girl, who was NOT good enough, tho I didn't know any better at the time.
Note that this thinking-logic is not Objectively Solid and unchangeable, but it bends to what you want (or don't want) it to conclude; some say Reason is a Whore to whomever's using it, so Reason can't be the ultimate judge of anything, at least not when it's about human beings. Normal Social Psychology (which I've taught) has created what's called the "Fundamental Attribution Error." That says that when I do something good, it's proof that I'm a good person; it's a consistent part of my personality. But when I do something bad (like one of those things I did that hurt one of my previous girlfriends, or even how I might have hurt my present girlfriend during the breakup we had over a year ago) it was just because I reacted to the special circumstances at the time, and it is therefore NOT a consistent part of my personality. (So my conclusions about MY personality are almost always self-serving.) But the other side of the equation is not equal: When YOU do something good I'll accept that that's part of your personality, IF I'm in the habit of liking and trusting you, but not if I'm suspicious of your motives. However, when YOU do something bad (that I judge to be bad or that hurts me), I DON'T ASSUME that's just a product of extraordinary circumstances, but instead that it's VERY likely to be a nasty part of your personality that I just never saw before--and now that I know it's there, I expect it to show its ugly face again, probably soon--because, in effect, it's consistently a part of your personality, so all you're doing when you're always good is suppressing that BAD part of your personality, that's bound to be still there. THAT'S the same thinking that's implied in your concern about "looking at her as damaged goods."
In contrast, Emotional Logic accounts for these attitudes much more sensibly. 1. We are always feeling something, and 2. what we're feeling directs our attention to particular perceptions or thoughts like shining a spotlight of a particular color--of which the basic ones are Excitement, Joy, Surprise, Distress/Sorrow, Fear, Anger, Shame(hurt/embarrassment/guilt/awkwardness/disappointment), Disgust(Dislike), Dissmell(Contempt), the spotlight colors can be mixtures. Thus our feelings always color our thoughts and skew them towards feeling-toned meanings.
So when I do something I perceive as good, I feel Joy (&Excitement&pride) toward myself--so obviously I'm a good person. When I do something ungood, I feel Shame (and/or Disgust), but if I shift my bad feeling towards external conditions--or the other person (like I did toward my first great love's ongoing betrayal, definitely hurting me), then I'll be OK with just being angry at something other than myself and therefore justified in not remembering that I did anything hurtful to anyone else. In contrast, when YOU do something good to me, I feel joy, etc. But when YOU do something bad to me, I feel hurt/disappointed/humiliated--I'm totally unable to feel the excitement and joy that are necessary parts of my loving you. I can't Idealize you (the natural thinking-colors resulting from excitement & joy/happiness). So your action (that's aroused my hurt&disgust) has robbed me of the idealizing thoughts I have toward you in order to marry you; I feel ripped off, and intolerably disappointed, so I'm ANGRY at you. I find myself believing your personality is permanently stained (by MY unerasable memory of suddenly feeling a surprise+hurt/disappointment). And I want to get that Stain UNDONE, so I can get rid of this horrible interruption in my ongoing excitement&enjoyment of you. The Deep Truth About Shame(hurt) is: Shame is triggered by the sudden interruption and impediment of Excitement & Joy, that does not eliminate E&J however. So you still have the fondest hope of returning to the UNINTERRUPTED experience of E&J, which is the purest possible experience of love.
That's where you're stuck right now, stuck staring your own disappointed Idealization of your partner in the face--that your hurt/humiliation shines onto her as a Stain on her personality.
I have to do something else now, before 5pm, so I'll continue this later. But back to the "Fundamental Attribution Error"--an error of "reasoning" as previously presented. It is also FUNDAMENTAL to human nature, that all of us do things occasionally that are 1. very self-centered & self-protective and 2. very hurtful to somebody else, because our personalities are NOT fixed in stone, so we let circumstances prompt us to do things we'd Disapprove of if we weren't strung out on stressful conditions and actually looked at our actions squarely in the mirror. I remember countless students (of the 2,000 or so) in my Psych of Relationships class that were CERTAIN they'd never violate their own romantic & sexual moral codes--and many were deeply wounded by the violations they'd witnessed or known that their parents had done. But I knew that over half of them would probably get to the edges your first GF reportedly reached, and a third or more would fit the definition of "cheating" or engage in what's now called an "emotional affair" by confiding in someone at work or online to the point of feeling more interest/excitement and enjoyment/empathy with that person than with their long-term partner.
If you grew up in a very moralistic household, like I did, you may have steered clear of temptation so far, so you could easily feel like you've NEVER done anything hurtful to a loved-one, tho that's more extreme than the version of that question that I asked you yesterday. But I think it's very likely that IF you could put yourself into one of your GF's heart, either a short-term girl or one of your two long-term GFs, you would find moments when what you did or said, or didn't do or say, DID hurt her. Even if you didn't want it to hurt her. Even if you didn't think she SHOULD feel hurt (but many, even most girls in her situation with you would have felt hurt too).
Why don't you to go back through your past in romantic relationships and see if you can find any moments where your actions might have hurt a girl (like fading away into the sunset while a girl is still expecting&hoping you'll want to see her again--esp After having sex). And especially remember that EVEN if the girl "shouldn't have expected" what she expected, or EVEN if the girl did something unkind to you ALSO, what you did that affected her COUNTS as an "insensitive & hurtful" action. [There's an interesting movie about the differences in "He Said, She Said" accounts of romantic relationships, before that one--it's called "High Fidelity" with John Cusack, and it's the flick where Jack Black gave his breakthrough performance with a song, so it's REALLY good.
Hasta manana, or at least luego.