This is an old thread, but I don't recall anyone saying confidentiality should be violated, or HIV positive folks prevented from training. But people, regardless of their HIV, or Hepatitis, or any other status, should avoid bleeding on the mat or others, and clean up their own blood if possible. All should wear gloves when cleaning up another's blood. Period. The chance of transmission is small, but it is there, and it is not worth the risk to you or your loved ones. Gloves are plentiful and cheap (I might recommend a non-latex powder-free variety if you want to go one step further, as many are now developing latex allergies from frequent exposure to latex in the health care industry).
Health care workers are more likely to get HIV from their patients than patients from their health care workers, although both risks of transmission are negligible. But there is no way I'd touch mucous membranes or body fluids without gloves on, except for life and death emergency... and even then, I pretty much make sure I've got gloves nearby (in my car, in my dojo bag, etc).