You don't have a claim to take to small claims court since you are not the one injured in this case. If you choose not to pay the bill, then the other person can then take you to small claims court for the bill.
Obviously, the person you left your name with acted on your behalf to notify the person of your intent to take care of the damage. Now,if it does go to court, it will depend on whether the judge thinks the documentation that the man produces is reasonable for repairing the damages. My guess would be that he will have sufficient documentation as he will have had sufficient time to get his facts straight. However, if the judge determines that all he did was install a 4 x4 post and is charging $20 in material and $227.51 in labor, then you may get a break. It is possible that he will not allow that type of mark-up for this repair. However, don't count on that. If the judgement goes against you for the full amount, then that is the time you can work with the court to determine a payment schedule.
With that being said, keep working with him and the person he claims did the work to determine the actual charges. I would continue the effort in regards to getting an actual invoice for this work. You don't want to go to court in this case since you may have the entire amount charged to you as well as any other charges that the person can come up with.
A lesson here would be that when something like this occurs, you really must take charge of the repair immediately. Otherwise, you can be somewhat at the mercy of someone that you don't know and don't know what they are capable of doing.
Pictures made of the damage and the type of material destroyed would at least have helped you from being responsible for upgrading the installation.