The presumption exists, IN EVERY CASE. Don't go overboard on this one like so many other naysayers. If one of these cases does come to trial, you are still presumed innocent, the government still has it's burden to prove that you possess an AW (like the law or not, they are charged with prosecuting prima facia violators) and then you are allowed to, under our constitution, confront witnesses, testify on your own behalf and present whatever defense you think viable, including that the weapon falls within an exception to the law.
Also, don't think for a second that a lawyer, a good one, would not be able to present the defense to a prosecutor before trial, probably before indictment (at the information stage), and pursuade him/her not to pursue the case so long as the defense is cut and dry. I have done it before and, at least in my area where LE and prosecutors have their hands full, such a strategy is often not only successful, but appreciated by prosecutors who don't want to waste their time on petit bullshit.
Using hypos like this as a catalyst for proclaiming our justice system DOA is absolutely silly. Real life does not work that way- and yes, there are travesties, like Randy Weaver's case, but they are not the norm. If they were, you would not hear Weaver's name used several hundred times a day to prove the same "point". You would see dozens or hundreds of others like it. My HO.