thx for your answer. to be honest, my question is applied to dogs in my case, but I'm curious for human cases as well.
So the answer is, without several parameters, there is a considerable chance of a false positive.
the original Scenario was puppies being vaccined, turning up sick a week after vaccination (there is a grace time of 1 week not to expose them to stress after vaccination), then being tested for common viruses (by a third party) which then turn out positive. I do not know exaclty how extensive viral testing is for puppies, I do know there are 2 kinds, a simple swap test with a positive/negative indicator (sort of like a pregnancy test), and a blood test where abnormal values suggest viral infection.