My first thought is usually to put myself in the kid's shoes. First of all, are YOU (i.e. the parents) able to get crackers any time you want, even before dinner? She did make that comment about wanting to be grown up. Maybe she wants the kind of freedom where she can meet her body's needs when she feels it's necessary, just like adults can.
Secondly, kids don't seem to react real well when parents ask things like "who did this?" or "why did you do this" or "did you tell the truth"...etc. All of it comes across as accusatory and probably makes them feel real defensive. I've seen it in other people's posts. Especially if there's usually punishment involved. Think of how it feels from their perspective.
Anyway, I was putting myself in your shoes, trying to imagine what I might have done differently. First, we don't have rules about "no snacks before dinner" except for sweets, and if I didn't think my son would stick to that, I would put those out of reach. If my son wants whole wheat crackers, he's welcome to it. It's whole grains; what do I care if he has them before dinner or during. I try to get dinner on the table early enough so that doesn't happen. Also, I may put fruit or crackers out mid-afternoon to prevent him from becoming really hungry just before dinner for precisely this reason.
Anyway (since you said you were stumped, I assume you are seeking advice here) how about this…. say you observe her with the crackers and you suspect she's done something she is not supposed to. You don't say a word; you calmly go about your business. Over dinner, if DD is not eating, you might casually ask DH or comment to him like "I'm surprised you told DD she could have crackers right before dinner." To which a most natural response would occur "I didn't." And that's all you need to say. Your DD would of course be observing this nonchalant exchange. Without you accusing or confronting, she is less likely to feel defensive, and may even confess (my son confesses all the time because nothing punitive is going to happen if he does. There may be consequences, but not punishments, if you catch the distinction. He doesn't feel threatened).
After dinner, without saying a word, you just put the crackers up out of reach. If they're going to be at kid-level with the assumption that she will follow your rules, then she needs to follow the rules. So up they go until she can abide by your rules. You don't announce this to her; you would just do it. Next time when she asks where the crackers are, you can tell her that since she took them when she wasn't supposed to, they're up out of reach for a while.
Another alternative, instead of waiting for her to notice that the crackers are now out of reach: You could sit with her just before bed (that's when I have "talks" with my son….it's quiet and peaceful and he's more conducive to hearing me & emotions are all done running high). I'd say something like "Dad said he did not give permission for having a snack right before dinner. When you are honest with me honey, it helps me to trust you and believe what you say. You want me to believe you when you say things, right?" ("yes, mama") So for the next week the snacks will be out of reach and you will have to ask us for them, until I'm sure you're going to follow our mealtime rules about this. And if your tummy is really empty and you're hungry, you need to let me know. I don't want you to be hungry and maybe we can come up with a solution so this doesn't happen again."
Now, I want to be clear that I don't think a huge amount of food-control is a real good idea. If you want her to listen to her body and not outside forces later on (i.e. peer pressure of all kinds) then perhaps she would benefit from listening to her body. If she's hungry, she eats. What's the worst that could happen? She doesn't eat all her dinner? I'm assuming that you don't make her clear her plate, right? We just ask our son to have "a balance"….he doesn't have to eat beyond when he's full, and we encourage him to have a little of everything just so his body gets a balance of what we've put out. But it's never a hard & fast rule. If he's full, he's full. And if he keeps blowing off dinner in favor of snacking on sweet stuff later on, we're wise to that and we tell him we're not going to buy sweets if that's his approach. We have tried to build a very trusting relationship. When he starts eating things at inconvenient times, or he eats things that are junky (to excess) we talk about why that worries us. We talk about the effect that certain foods have on the body, on our behavior and how we feel. So he knows we're not being arbitrary. (in case you were wondering, he's 8 now but we have taken this approach for the past several years, after an initial rocky "because I said so" approach when we were new parents) :-)
Anyway, I just think her hyper-drama you talked about can be avoided with a change in how you approach it, so maybe she feels that you're being fair because you, in fact, are.