My guess would be that dead Liberian and his family were taking effective precautions even before they took him to the hospital. All of the interviews I have seen of his relatives indicated that they already thought that his symptoms indicated that he had contracted Ebola before he received the correct diagnosis.
When the story first broke, there was a timeline of events, which described one of the relatives as a nurse’s aid of some sort...and it went on to say she ‘sprinkled’ bleach on the furniture.
And, it also recounted how she went to the store to buy Duncan a $50 blanket - which I find interesting. Apparently she didn’t want to contaminate any blankets they already owned?
It seems this family strongly suspected he had Ebola, and took precautions. Even the fact that Duncan somehow scraped together enough money to fly here indicates that he knew he may be infected, and had to get out of Liberia right away.