It's even worse than it first sounds, because the good candidates get hired, but the candidates that get screened out by the fizzbuzz tests don't exit the scene

It's even worse than it first sounds, because the good candidates get hired, but the candidates that get screened out by the fizzbuzz tests don't exit the scene - they move to the next company along to try again. So although the people in question are a minority as a proportion of the population, the amount of fraud you need to filter out in practice is high, and the people you most want to filter are continuously practicing getting past initial quick filtering steps.