I honestly don't think anyone actually believes that, it's just spouted out as an inside joke. (I even joke about it often but don't believe it.) I remember seeing a thread on another forum pointing to another real life disease with matching symptoms and everything, but I could never find it again :/
EDIT: Did a quick search on the matter, I found what is very likely the page I accessed earlier, and it's not forum, but it is Naruto-related.
You must be registered for see links
^This is actually the most compelling theory I've seen about Itachi's illness.