There is the famous "Window Period" problem though. When the virus first infects a person, it spreads and replicates throughout the body. It takes a few weeks for most people to have made measureable amounts of antibody, so if someone was infected a week ago, they may have sky-high levels of infectious virus in their blood, but they will test "negative" for HIV antibodies.
At STD clinics in New York and Seattle, investigators have tested HIV tests that don't look for antibodies, but for the virus itself. Tests done on people who had a HIGH risk exposure, i.e. unprotected anal sex were tested. About 2% of gay men who tested negative with antibody tests were positive for RNA tests.
These men were acutely infected, and probably very contagious, but they could put "HIV Negative, as of today" in their on-line profile, in all honesty.
RNA tests are good for picking up acute infection in men with a high risk encounter, but are not good for screening the general population. In this case, though, they show that when someone says they are negative, there is a real chance, albeit small that they are wrong.
