That seems like a testable hypothesis. If statistics on deaths by pneumonia and similar illnesses are recorded, and aren't so high as to dwarf HIV deaths, then there should be a noticeable spike in those deaths during the HIV years. One could compare that spike to the U.S. to see if Cuba's HIV deaths were underreported relative to the U.S.
I think, anyway. I'm not a statistician, but it feels like it should work.
If statistics on deaths by pneumonia and similar illnesses ... aren't so high as to dwarf HIV deaths
I'd guess that in poor non-African countries that's a very big if.
A post from Gregory Cochran's and Henry Harpending's excellent blog West Hunter.
The commenter Ron Pavellas adds:
The Wasserman Test.