If you rent from Thrifty Rent-A-Car and have an accident, whether it was your fault or not, and whether you purchased their damage insurance or not, you will be billed for thousands or tens of thousands of dollars by Subrogation Management Team (SMT), which handles damage claims for Thrifty. Even if you don't have an accident, it is not unusual for SMT to claim that your rental car had damage that you failed to reveal, and bill you for its "services".
 As discussed in this article and this report, there isn't much you can do to avoid this (censored) after the fact. So if you value your money, your good name, and your good credit rating, never, ever do business with any car company (such as Thrifty) that works with a "third-party" claims agency, such as Subrogation Management (hereinafter referred to by the more accurate Satan's Minions). Before renting a car, contact your insurance company to find out which rental companies they consider honest and above-board, and rent a car from one of them. It may cost a few dollars more in the short term, but could save you tens of thousands of dollars in the long run.

Further Advice About Satan's Minions
 Since posting the above, I have been contacted by several people who have dealt with Subrogation Management. The following is a summary of information received so far (warning — consult with your lawyer as to the accuracy of the information below before taking any action based on it, as laws may vary from state to state):
 (1) SMT provides their "service" for many rental car companies, so as noted above it is very important to contact your insurance agent to find out which companies you can safely deal with before renting any car.
 (2) (really scary) SMT may bill you even if you do not rent a car, if your vehicle is involved in an accident with a car rented by one of the companies they collude with.
 (3) There is considerable question about the legality of sums claimed by SMT (this will not keep them from pursuing you, hence the advice about consulting your lawyer):
  (3a) If Satan's Minions contact you they will claim that your signing a car rental agreement with one of their clients obligated you to pay their charges. But since as noted in item 2 they also bill people who never rented a car or signed a contract at all, their pursuit of these charges has nothing to do with the contract itself, but is merely an attempt to frighten you into paying whatever they claim you owe them.
  (3b) Even if the charges were valid, to have any legal effect upon you (other than paying your lawyer for advice and defense) they must be proven in court as follows:
   (3b1) As to "loss of use" of the vehicle, proof is required that the rental car company had absolutely no vehicle available to rent on the days in question as a result of the unavailability of the damaged rental car. If there was even one car available to rent, the fact that the damaged rental car was out of service is not a provable loss of income to the rental car agency.
   (3b2) As to "loss of value" of the vehicle, proof is impossible until the vehicle is sold, and nothing is due until such time. Even then, unless it can be proven that the vehicle sold for less than it otherwise would have, no loss will be upheld in court.
   (3b3) As to "administrative costs", such fees are only legally due if it can be proven that SMT's actual cost of pursuing the matter exceeded the fees paid to it by the rental car company, and even then only if you actually signed a contract with the rental car company agreeing to pay said fees.
 (4) Whether you consider any of the above useful or not, you should at least send Satan's Minions (whether employed by SMT or some other company) a written request that all communications from them be in writing, and insist they not phone you or anyone else. This is a legally enforceable right, as a matter of privacy. (It wouldn't hurt to mention that your lawyer needs hard copies of all correspondence, as it would put them on notice that you are as prepared to play hardball as they are.)