Per Wikipedia, Down's syndrome currently occurs in ~1 in 1000 live births, and used to occur in 2 in 1000 live births some decades ago, in the USA. That means that a test with a 1% false positive rate (99% accuracy) will lead to a false positive for 98-99 healthy embryos per 1000 live births. I would say that this is fair to call "not all that accurate".

Note: I am not in anyway saying that this means that people shouldn't trust the tests, or anything like that. Just reminding everyone that a test's accuracy has to be compared to the incidence of the disease to decide if it's high or not.