Well, special in two senses: First, in the canonical formula for Gaussians, sigma appears directly. For the case at hand, the confidence limits associated with 1 sigma, 2 sigma etc. in physics match exactly the area under the curve for a Gaussian integrated +- said sigma around the mean. That's were that connection actually comes from, and a physicist will always think: Within 1 sigma? That's 67%.

Hearing 99+-3% is a very strong indication that the person used an incorrect way to determine the uncertainty, most likely by taking the square-root of counts. But you are right, if the efficiency would be around 50%, that approximation is not so bad.