I know that you can have false positives, but you can't have a false negative. I was told that by a vet. If the antibodies are there, they will test + for either disease.

I don't know how many false positives there are, but I think many times they test positive when they have been exposed for a period of time, have been bitten (most adults testing positive are stray males) or are born with it. Most of the cats I know that have tested positive STAYED positive. I've only known of a few FIV+ cats that actually tested negative later on (they had basically contracted the antibodies from their mother, and the body fought it off).