There's no need to get overly legalistic. The fact that the incident is AA's fault does not mean that AA is liable AA's COC are clear:

American assumes no liability for articles carried in the passenger cabin.

Thus, AA is dealing with this as CS matter, not legal liability and the further you push into the legal arena, the less likely satisfaction becomes. This stuff happens all the time and AA (and other carriers) have expected ranges for what's reasonable. No need to demand copies of reports and such.

If there is permanent damage, submit the particulars. If there isn't, it's just an annoyance, but remember that AA doesn't bill you when you spill a drink on its seat !

It's helpful when dealing with a business such as AA to have sorted out what they must do as opposed to what they ought to do. Here, where AA has no liability, the manner and reasonableness of any request will go a long way to satisfaction.