I can't even imagine what you and the owner of this dog are going through. Like you, I have a secure 6 foot fence around my entire property. During my time as a sitter, I can think of four dogs that were able to jump my fence and escape from my yard. These were all first time clients, and none of the owners were aware of their dogs' jumping abilities (or chose not to mention them). Some people honestly don't know their dogs can jump fences because they live in apartments.
Luckily, none of my "fence jumpers" were injured, nor did any run off. However, I did not accept any of these dogs again because they were too much of a liability.
As Jean and Ray mentioned above, we learn from our mistakes. If you decide to continue sitting, I would recommend staying outside and closely watching any guest dogs- at least until you get to know that dog very well and know for a fact that he cannot escape the yard. I would also close off the doggie door while dogs are staying with you, even if the owners say they're ok with it.
As far as reviews go, a poor review will impact you severely if you're relatively new to sitting and don't have many yet. If you've been sitting for awhile and have multiple reviews, there's a chance that potential clients may not see it. I've had a couple situations where dogs were injured and had to be taken to the vet. I covered the bills in both cases, and the owners both understood that accidents happen. Neither gave me a bad review, and one is still a repeat client. You handled your situation in a kind and professional manner. I doubt the client will leave a poor review (or at least not a detailed one) knowing it would end your dog-sitting career.
Best of luck hun:)
Thank you everyone for your comments and advice. I truly wonder how the family is doing. If they ever leave a review, good or bad, I still think the world of them.