The article doesn't seem to be complete and there's too much references and too many variables. So yeah, I definitely understand your position.
Then about the study, the number may be inflated because of multiple probable causes of death but I think that the people who made it took a blood sample on the corpses and if they contained HIV antibodies, that meant they had AIDS and died "from" it (from the study's point of view). It's not illogical for me that they thought that way. It's true that nobody directly dies from AIDS because it's the opportunistic infections that do the lethal work. AIDS is a state, a syndrome. But the presence of HIV in the body will necessarily lead the infected to AIDS and antiretroviral medication can prevent that or at least slow the transition down greatly. Then knowing which infection did the deed is a matter of point of view.
HIV, by decreasing the body's protection, is like a Trojan Horse. It doesn't kill, but it weakens the castle's defense and then ease the access to it for the belligerent army. Then does it really matter to know which corps, or which solider killed the king ? When the front gate is down, and the army is in, it's over. If it wasn't for the Trojan Horse, nobody would be in (or not that fast at least).
I think that what the study was about IMO (I won't lie, I didn't read it, just looked at the charts) : all the deceased had HIV.
Did they have AIDS, were they close to have it ? Far from ? Did they have another lethal disease ? I don't know but I don't think that's the study's point.