I don't buy that at all.
Only one of my cats gets vaccinated against FIV, and has had boosters for the past 3 years. 6 months ago, he got a cat bite abcess and I decided to test him *just in case*. He came out negative. We have tested many cats with negative results that have been vaccinated against the disease.
I have no idea if the US vaccines do this to a cat, but its certainly not the case in the UK. Very shortly after vaccination, a false positive can show, but I've never experienced this.
It is sad that positive cats are euthanased, but I see why it has to happen. It happens here too. It displays the importance of microchipping, IMO.