Well it was a while ago now but here is an update. I did receive the dreaded FedEx package (it took two weeks for the background check to clear after accepting the offer and filling out he application) and waited for a phone call (that took another week). I did get approved in the end and I will be relocating shortly.
The dismissed case did not come up in the background check. I think that a dismissal showing up really depends on how your local courts handle them and wether or not they will disclose that kind of information. Technically it will always be on record, even if there wasn't a conviction. Some states do have processes for removing any record of what happened, even convictions. Look into your local laws and talk to a lawyer.
Bottom line is that it is always better to disclose and have them not find it, than the other way around. I actually talked with the person at Boeing security about the vagueness of the question. She said they are considering rewriting it, but suggests that anyone filling out the application discloses everything. Even if a case is dismissed (or deferred and then dismissed) they might find it. Depending on the offense, if they see that it was deferred and eventually dismissed, they still might disqualify you for it. They can and will see deferral dates and dismissal dates. So it is a risk, but if they find it and it wasn't disclosed, that is pretty much a guaranteed disqualification.