It isn't always that the test has a false positive or false negative. It's the nature of what the Elisa test is looking for and the nature of FeLV. If cats are exposed to FeLV, they'll take the virus into their system and the body tries to fight it off. Elisa tests for exposure to the virus that causes FeLV, not that they actually have the disease. That is why the explanation above says "transiently infected". A cat usually fights off the disease in the first 30-45 days, which is why they suggest that you retest. If a cat hasn't fought it off during that time, it usually remains positive because either a) the virus exposure has turned into real FeLV or b) the cat was exposed again.
Only an IFA test can prove or disprove FeLV. The problem is that most vest are not up to date in their practices and don't run it.