Yet the idea of eliminating HIV is so appealing, and the benefit to humanity so huge, that scientists and policy-makers are seriously considering the concept, albeit on regional scales. In the next few months the World Health Organization (WHO) will meet to discuss how the idea could be tried in developing countries, and something approaching elimination might be attempted in the UK within the next decade. "You could eliminate transmission overnight," says Marcus Conant, an HIV specialist in San Francisco.

Read on the interesting article.

Why would someone refuse to be tested if it meant they could be cured.

If they were sure they are not sick, is one reason...

You can bet religious crackpots would find some reason to be anti it. Conspiracy theories. Sensationalism. (Did you ever read about the 12 Japanese students who died/suicided after tammifly shots?) Ignorance. Guilt (that they may have it because they had sex with someone who had body odour.)
Plain old ornorary.
You name it and half the population will cooperate. The other half vacillates.