Yeah, he was treated badly.
He lied, really? That woman he helped had malaria, according to her family. Malaria is common in Africa, and people die of it all the time--around 600,000 people, in fact. So if she died of what he thought was malaria, and he later said he had no contact with anyone who had Ebola, how is that lying?
The hospital should have admitted him the moment he showed up with a fever and said he came from Liberia. Since the hospital didn't, and survival chances are increased if treatment is started right away, his family *does* have a case against the hospital. On the experimental drugs, they don't have a case, because there is no proof that anyone who survived did so because of the drug. He received an experimental drug, too. There are reasons a drug like the one he was given probably wouldn't work--but no one in the general public is going to know that, or understand the reasons.