What Vietnam did, was to immediatly quarantine anyone who showed any symptoms of SARS at all. For all intents and purposes, they also banned the word. If you were caught saying "SARS", you were arrested.
One way to convince others you got rid of a disease is to stop talking about it or acknowledging it publicly. I don't know if this means they did things right and actually are *rid* of it though.
My first thought was they probably killed anyone discovered with the disease.