John,
there's hardly any disease in which there is only one agent (a few genetic diseases). So the interesting question to me seems to be whether HIV is a necessary condition or not. It doesn't seem to be a sufficient condition (but that's extremely rare in medicine, see above). I only know a very small part of the literature and all of that is second hand (reviews, overviews) but many seem to agree that 'yes' is the correct response that is only persons with HIV may get AIDS. And to the best of my knowledge there is no other candidate for a necessary condition.

As for the second complex, yes, I have seen similar claims (old and recent) in psychology (and sad to say, they are basically correct). Misuse of statistical tests is common, less so by doing the calculations wrong, but more often so by doing the interpretation wrong or by using a wrong test. Whether you come to 60% wrong statistics depends upon several decisions you make in a metaanalysis of the statistics used in studies. Do you count a study as flawed if there was one of many tests wrong? Do you count it as flawed if the wrong test was used (though the conclusions might still be valid, since many tests are rather robust against violations of test assumptions)? Do you count it as wrong if you did a test that does not support your theory but the theory would have been supported by the correct test? And so on.

But I've never seen so many wrong statistics as in studies of the paranormal, especially in astrology and studies on the power of prayer. There are studies that are know since decades to be completely wrong and yet they are cited until today be the believers. But sloppy research in parasciences is no excuse for sloppy research in mainstream science.

Wolfgang