That parenthetical doesn't quite work for me.
If synthetic data always degraded performance, AI labs wouldn't use synthetic data. They use it because it helps them train better models.
There's a paper that shows that if you very deliberately train a model in its own output in a loop you can get worse performance. That's not what AI labs using synthetic data actually do.
That paper gets a lot of attention because the schadenfreude of models destroying themselves through eating their own tails is irresistible.