-> Human evaluation does not agree that PBSMT is more accurate than NMT. Sure, the fluency/"sounds good" gains from NMT are much larger than the accuracy gains, but evaluations I've seen put NMT ahead on both metrics.
Before, I could skim outputs, and get a fair idea of which areas were poorly translated by where it was garbage. Now, I get the impression that (like with GPT or style transfer) something always comes out, whether it's related (or even necessarily has the right negation parity) or not.
And it is also worth noting (as you've sort of mentioned) that appearance of fluency can bias translators who are instructed to just evaluate accuracy, or to evaluate accuracy and fluency separately. There is ongoing research into that problem.