Can God, if S/He exists, cure people? Or is it just the penicillin doing the work?

Some say God can heal. But He/She can't heal amputees. At least he has never done so despite all the prayers. I guess amputees aren't worthy of His/Her saving grace.

In Ohio, televangelist Darlene Bishop is being sued after she told her brother God had healed his throat cancer. The brother stopped taking his treatments and spent the last years of his life being cared for by his sister. He died of throat cancer 18 months ago. Bishop even wrote a book Your Life Follows Your Words, wherein she describes how prayer cured her breast cancer and her brother's throat cancer. The book doesn't bother to mention his death. Her brother's family is suing her for wrongful death and for mishandling her brother's estate.

In her defense, she claims the book was published while her brother's cancer was in remission, and after she found out it wasn't, she advised him to follow the doctor's advice but he refused.