"First of all, forget all the letter writing to these various agencies. At best, it gives some governmental statistical freak something to do, but otherwise is blowing smoke. Your contract of carriage is with the airline; the airport authority, departments of transportation (in either country) are irrelevant.
Trust you have photographed the damage.
Your claim needs to be sent in 2 directions:
1. The insurance carrier from whom you purchased this excess value insurance. What is a ""ticket agent?"" did you buy this from the airline's ticket staff at the airport, or was this a policy sold by a travel agancy? My experience is that airlines are not in the insurance sales business (although some of these travel insurance companies have been known to set up incentive programs with airline ticket offices), so this is some ""aftermarket"" policy. If so, it should not be the airline's judgement as to paying out. Read that documentation.
2. AA's customer relations department. I would not expect that staff at the carrier's baggage service office at the airport is empowered to settle big claims. If you have not done so already, write AA's customer relations department, provide documentation as to the value of the bike. This gets a paper trail. When they reply and blow off your claim that BICYCLE could not possibly be worth $3,000, call them and speak to a manager. Here at SWISS, we follow the normal standard for international baggage claims which compensates by WEIGHT (peanuts per kilo) for lost or destroyed baggage. Yours was an international flight and you may be offered the same. When I referred to contract of carriage above; this is in the fine print of your ticket. Any compensation above this is probably the result of your negotiating skills and ability to provide good documentation.

Good luck and sorry for your loss

P.S. You can get some money out of this; we have settled a few of these claims ourselves...I've been consulted by our customer relations people about valuations.
"

"There is probably no such thing as ""airline approved."" Airlines cannot sit together and approved much of anything. Probably this meets a generic size limitation.
Here at SWISS, we are probably similar to most carriers' policies on the North Atlantic (not the same to other regions):
Size: 70 linear inches (length+width+height)
weight: 50 pounds for economy class

Some bike cases exceed that 70 inch thing, hence the sidebar wherein it reads that a bike boxed in a hard case counts as one of your 2 permitted pieces of baggage, even if it exceeds the 70 inch noted above.
Or you get a checkin agent who only knows domestic rules and nails you for an excess baggage charge.

Know the carrier's rules before you pack."

If you are an AA Advantage member call 800 433 7300 and speak with customer service. I have found their people to be very helpful to me in the past. Perhaps they can suggest another course of action you can take.

You might save any TSA inspection notices, as TSA may have opened the suitcase and unpacked and repacked your bike. There are some stories circulating about damage to repacked bikes after TSA allegedly improperly repacked the bike after inspection. The advice is to have the inspection in your presence, if possible, so that you can observe the repacking. This also introduces the situation where the airline and TSA can point fingers at each other and say it is the others fault.

Also, we had a claim denied for luggage damage during a recent flight because we left the airport without reporting the damage. I guess that means that you have to do a full inspection of the bike before leaving the bagagge area. When I ship my bike now, I take close-up digital pictures of all the tubes, packing and boxed bike to back up any claim that needs to be made. The last two times I shipped by FedEx and didn't have any problems with damage.