FUJISAWA, Japan — Wilmette, Ill., native Maggie Shea had been telling herself this was just another sailing race in a lifetime of sailing races. Then she saw her boat. Per tradition, the skiff was rebranded with the Olympic logo and “USA” along the side. The gennaker sail, which typically bears a sponsor’s logo, was now emblazoned with a 270-square-foot American flag. Shea put her arm around her teammate, Stephanie Roble, and took in the moment. Friends since they were teenagers on the Midwestern racing circuit, the duo marveled at what they had achieved as a team. “We’ve been sailing together...