I’ve never gone through this particular situation myself, but I have had some success with responding when Amazon doesn’t seem to grasp what I’ve already told them. I would approach it something like this:

(Sentence #1 - make the point CLEARLY at the VERY beginning and in no uncertain terms)
This complaint has been filed in error and the complaintant is FALSELY claiming he owns the rights to product xyz widget. Supporting documentation attached.

Supporting documentation includes:

• Letter of authorization from the TRUE rights owner for product xyz widget. The TRUE rights owner is (rights owner name). Attached please find letter from Mr/Ms (CEO Name), CEO of Company XYZ Widgets, the TRUE rights owner of product xyz widget.
• Point # 2
• Point # 3

Many times the person reading will already assume you did something wrong, and only read far enough to see that you haven’t offered any solution. So your first statement should make it clear that the problem is a FALSE claim against you. Then immediately move to outlining why.

Don’t give them any chance to think anything other than that the complaint was filed in error. Don’t expect them to read through your whole appeal to reach that conclusion. Don’t expect them to draw any inferences, or reach any conclusions on their own, at all. Lay it out for them like they’re 5 years old. State the main point first, then provide supporting facts.

You want them to understand the gist of your appeal in the first sentence or two, and prompt them to want to read further. Your documents should absolutely support your case, but it’s possible the reviewer didn’t look at them or understand why you were sending them. If that’s what happened, the above approach should get it through to them.