Should I pay a bill for a service not performed and then performed at another hospital? The other hospital got paid.

My wife went to surgery because of an advanced case of gallbladder stones. The doctor that removed the gallbladder did it quick and without problems but then found out that one stone was stuck in the bile conduit that goes to the intestine. Because he was not the one to perform that type of procedure another doctor was called that initiated another procedure after getting all the info. He could not have it done and my wife was scheduled to go to another hospital where they are used to perform this type of surgery (Duke Hospital). They did it great and got paid for it. My question is: After all the bills should I pay the $1,200 bill that the doctor sent without any result and even making my wife to suffer more? is this fair for someone to have to pay when a person is not qualified to do it or doesn’t have the correct equipment? Sending to another location and then everything goes fine shows that he should not have started in first place. Thanks for any info!