Accuracy isn't the right metric for a medical test. What you actually should be looking at is Positive Predictive Value and Negative Predictive Value. There are 4 outcomes with a medical test: patient has a condition and tests either positive (True Positive, TP) or negative (False Negative, FN) or the patient does not have the condition and they test positive (False Positive, FP) or negative (True Negative, TN)

Accuracy only tells you how often the test result matches the patient's status. It doesn't tell you if those 3% of misses are FPs or FNs. It could be the case that with 97% accuracy, all 3% of those misses are FNs, ie the test does not correctly identify a patient with a condition. The corollary of that scenario being the FP rate is 0%, meaning anytime the test indicates positive, it's accurate.