For any Celiacs actually reading this blog, I came across a link to an article regarding various auto-immune disorders and possible false positives for AIDS. Personally, I have Epstein-Barr Virus on top of Celiac Disease. EBV is listed as a possible cause for false positives. Oh, joy.
The article is from 1996, so there is probably a lot more current data, but it's an interesting read. There are a lot of illnesses that might throw off the readings.