Here's another update. I called budget, and then on to their insurer, and they tell me that there's no damage claim on file. I asked the lady on the phone if I need to do anything, but her searches based on my rental agreement return no results. Her words are "maybe they decided not to proceed with the claim." I asked for something in writing, and she advises that I have to call and get something from Budget directly.
So damned if you claim, damned if you don't. Amex on the other hand is trying to help me settle the claim, but I have nothing to pass on.
Life is good