When you go to the hospital, you expect that the hospital did its due diligence in determining the safety records and backgrounds of its doctors, nurses and other staff members. If you get hurt and then find out that the background check was never performed or that the doctor had a long history of errors, you would have every right to be angry and to seek a claim for the hospital's negligence.
Any health care facility worth its weight will take time to do background checks on anyone who is a candidate for employment. Even in the best-case scenario, a hospital faced with a medical error is responsible for the provider's mistakes. It's in the hospital's best interests to make sure anyone hired isn't negligent or known for making errors that result in litigation.
Additionally, a hospital that doesn't do a background check can be sued. Imagine knowing that you could have avoided a serious health complication if you'd known that your doctor had made the same error in several patients before you. You'd have wanted to know, and you probably would have chosen another provider. That's what the hospital takes away from you by not doing a background check on the doctor or staff member it's hiring. That's why you have a right to sue the hospital in question.
Your attorney can help you collect evidence and use it to negotiate a settlement with the hospital. If the hospital will not settle, then there is a chance your case may need to go to court for a jury or judge to rule on it.
Source: The Hospitalist, "Background Checks," Lisa Ryan, accessed March 15, 2017