The sad thing is that a cursory glance at the histories of AIDS and of antiviral medications renders their bizarre conspiracy theory absurd.
In 1981, AIDS was officially recognized by the CDC and a few years later the connection to HIV was inarguably established in 1984, which created lasting international concern.
The first US approved antiviral effective against HIV was Zidovudine (also known as azidothymidine, AZT for short, and marketed as Retrovir), approved by the FDA in 1987. Now, one interesting fact is that AZT is notable for its amazingly rapid development and adoption, only taking just over two years to go from first demonstration of effectiveness to approved usage.
Modern antivirals are designed specifically to inhibit the chemical processes that allow for a virus' reproduction. However, AZT was developed before genetic sequencing was possible on an efficient scale (the first fully automated DNA sequencing machine, the ABI 370, wasn't available until 1987), and therefor before virus reproduction and the chemical processes involved were fully understood.
Consequently, AZT was developed using the old fashioned methodology of trial and error using various substances to see if they worked. This empirical methodology is no different than that used in the discovery of any other kind of traditional medication - we learned that aspirin helps against headaches and that penicillin kills off bacteria by trial and error, and the same applies to AZT.
But what about that super rapid approval of AZT? Surely that's suspicious? Well, it would be if AIDS wasn't one of the biggest international controversies of the 1980s, and if there wasn't a mad dash to try to find treatments for the HIV that had just been inarguably proven to be the cause of the illness. And when AZT proved to work incredibly well without major side effects, it got fast tracked to market to help what was, at the time, quite literally a pandemic.