It seems to me that the biggest problem you have here is that they claim that your valves were BENT before you came into their shop. The reapir of these valves is where the big money is going to be. Whether the valves were BURNED was, as I understand it, not part of the original problem. There would have had no reason to have pulled the heads and discovered the burned valves unless they had bent the valves in the first place. The term 'burned valves' should never have even been mentionesd regarding changing a timing chain.
By saying that your valves are burned they are trying to justify removing the heads where they 'accidently' found bent valves. They are on a fishing expedition for reasons to 'discover' bent valves and cover their incompetance.
I think that you are in for a big surprise when you see the repair bill for your car. I think that I would talk to a lawyer before I pick up the car. Once you have taken delivery of the car you have in effect accepted the repair shop's version of the story. Once you accept this version it will be difficult to make a claim and you will have much less recourse under the law.
If this situation becomes legal be sure to ask for proof of the mechanic's conpetance, i.e., diplomas, certifications, etc. Make the repair shop prove that the mechanic is qualified to work on your car. Talk to other mechanics about how the timing chain should be replaced and write it down. Ask the mechanic how, during the proceedure, he would prevent the engine getting out of time. How many of these jobs has he done and can the shop prove this?