This is a remarkably common fallacy when interpreting false positives, false negatives, or sensitivity/specificity data. It's a shame Bayesian statistics isn't more commonly known as it's a good way to avoid the misconception.

Simply put: extraordinary claims demand extraordinary support.

If the prevalence of PGD is very low, you need a great deal of weak tests showing positive results or a hypothetical extremely sensitive and specific test showing positive results. Both routes are difficult and expensive.