The Short Version
The claim is well-supported. CDC NHANES data shows median body fat of 28% for men and 41% for women, meaning more than half of both sexes exceed 20%. Since obesity rates have only risen since this data was collected (1999–2004), the claim holds as a conservative estimate. However, 20% body fat is below the healthy range for women (21–33%), so exceeding it is normal and expected for most women — the claim is factually accurate but could mislead readers into thinking this threshold signals poor health for everyone.