I'm not sure that's how it works when it comes to accuracy of medical screening devices.
Say if there is a device that offers 99.9% accuracy but is used to screen a disease that occurs 1 in 100,000, then applying your logic would mean out of the 100 people who were identified positive, only 1 actually was accurate, thus makes the actual result of the device 99% false.
The 85% here is likely to refer to that out of the positive results, there is a 15% false-positive rate.
Medical screening device accuracies aren't calibrated to how rare the actual disease is.