No, it's up to the prosecuter to prove that the rifle is in AW configuration, and that he has reason to believe that it is not a grandfathered pre-ban. It is then up to the defendant to provide some kind of evidence that the gun qualified for the grandfathering provision. Date of manufacture of the lower is not enough to qualify; the lower had to be in AW configuration (this can include being in the same box with a parts kit that had enough AW features) before the ban, and be legally possessed, in order to be grandfathered.
If YOU were the owner on 9/13/94, you can testify that you have first-hand knowledge of its configuration, and that *should* be sufficient. If you were NOT in possession of the rifle on the date the ban went into effect, you would not be able to testify, as your testimony would be considered heresay. In that case, you'd need some kind of evidence (generally paperwork) that could be submitted to the court to prove your defense.
A letter from the manufacturer works. So would an affidavit from the person who possessed the rifle on 9/13/94. A serial number list from a website is NOT going to be considered proof in any court.
Someone will say "the law doesn't specifically require paperwork", and they'll be right. Nevertheless, the paragraph above describes how the case would be handled in court.
It should be noted that, so far, very few people have been charged for AW "configuration" violations alone; most of these charges accompanied some other charge, and the prosecuter added everything else he could think of. So far, there seems to be little overall interest in enforcing the law on "Joe Average", though with Project Exile, that could easily change.
-Troy