While not legal advice per se, you may find the following link helpful in deciding how to handle the matter. http://www.progressive.com/understanding-insurance/entries/2009/8/31/who_pays_for_towing.aspx
Additionally, if the towing company refuses to assist or even process the claim, your carrier (especially if it also AAA) may be willing to waive the deductible given the fact that it was their agent or subcontractor that caused the damage. Also, if you can prove the damage was caused by a negligent act of the tow truck driver for example, failure to secure the car properly, dropping the car, speeding over a dip causing your car to bottom out, etc... you have a better chance of negotiating with the towing company.
If you do get stuck with the deductible, Small Claims court may be another option to you.
Disclaimer: The materials provided below are informational and should not be relied upon as legal advice.
I agree with my colleague. The towing company was a bailee of your vehicle and had duty of care. Therefore, the two company must cover any damages to your vehicle which occurred as they has possession of your car. Put in your claim to the towing company and to your own insurance company. If they both refuse, you need to bring an action before your statute of limitations runs. Be sure to consult your own attorney to protect your legal rights.
Your insurance company, after covering the costs to repair your vehicle, will be able to go after the towing company to pay the bill. You should ask your insurance company to waive the deductible, they likely will in such a case.