No, they were responsible for their own deaths. They may have died quicker, but they did not die because of.
You assume that being HIV+ is a death sentence. Have there been studies of the progression of the disease without treatment? Do we even know if what is thrown into the list of symptoms are attributable to the virus?
Just like Covid 19, all things that happen medically to a person that is HIV+ are attributed to the virus. Pnuemonia, TB, cancer, blood clots, strokes, sepsis and more are said to be the result of HIV and CV-19.