While dancing excerpts of August Bournonville's Napoli this summer at the Massachusetts-based Jacob's Pillow Dance Festival, the artists of the Royal Danish Ballet were in perfect sync. The dancers exuded pure cheer, from their buoyant, clear footwork to the precise angle of their épaulement. This seemed fitting for a national company where most members train in the Danish style from age 7 and feed in from the school. Yet three of the principals onstage—Amy Watson, J'aime Crandall and Holly Jean Dorger—are in fact American.