In the early 1990's and late 1980's this would have been a true statement. However, as my children sometimes say, "Times have changed." Most if not all AIDS patients in the industrialized nations have been tested for HIV infection. Nearly all AIDS patients also have HIV. Even in Duesberg's article only a few thousand AIDS patients are HIV negative. Early on the only screening test available was a blood test for antibodies to HIV. A screening test is a test that can be performed on large numbers of people because it is relatively inexpensive. This test was not very sensitive. In other words it takes a lot of antibody being present in the blood to HIV to get a positive test.
This blood test is still used today and is called an enzyme linked immunosorbent assay (ELISA). Since this test is not very sensitive many people are encouraged to come back and get tested again at a later time. This waiting period allows the person's body to make more antibodies to HIV. Most people will eventually make enough antibodies to HIV and if infected with HIV will test positive via the ELISA test. If in some rare cases a person infected with HIV never makes enough antibodies to the virus we now have a way to detect very small amounts of HIV RNA in the blood. This virus doesn't make DNA as its code for life. Instead it makes RNA. This test called a Reverse Transcriptase Polymerase Chain Reaction (RT-PCR) actually finds the minute amounts of HIV RNA in the blood. During the test HIV RNA is copied to DNA and then many many copies of this DNA are made. After making these HIV DNA copies other methods are used to show the copies have been made and to determine how many different HIV RNA molecules were in the blood sample.