By week 20 there is practically no chance you're not going to know if you're carrying a baby with downs or not unless you refuse all the modern screening/tests available.
NIPT tests can be done at week 8 and give a very high indicator that can be followed up with close monitoring/invasive tests at week 14-15 that give a 99% accuracy. That's hardly "are really not that exact".
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.
Screening ‘test’ vs diagnostic ‘test’ is an important concept.
Screening tests are designed for sensitivity — false positives are expected and identify who would benefit from additional diagnostic tool and procedures.
NIPT tests can be done at week 8 and give a very high indicator that can be followed up with close monitoring/invasive tests at week 14-15 that give a 99% accuracy. That's hardly "are really not that exact".