Unless the damage was very extensive and very costly, you would be better served getting the damage repaired rather than preparing a court case. A successful court case is unlikely to result in anything more than the cost of repairs, and even a small claims case can take considerable time and effort with a possibility of not succeeding. You have successfully put the auto repair facility on the BAR's radar and the facility knows that. The possibility that they are going to engage in anything fraudulent at this point is exceedingly small. They have no way of knowing whether you might be participating in a BAR "sting" (very common) and few if any facilities would gamble with that at this stage.
I disagree with attorney Chen about issuing a subpoena for BAR's file.They are likely to resist that effort with full legal process and then you are in for an expensive, time-consuming and potentially unsuccessful fight.
I recommend that you talk to a BAR staff person about the facility's offer and follow the recommendation there. Try not to get caught up in the "contest." A satisfactory settlement that makes you whole in terms of your financial loss is ALWAYS better than even the best lawsuit.