Velocities measured in turbulent boundary layers over yawed flat plates confirmed that the mean velocity profiles normal to the leading edge are proportional to the velocity profiles parallel to it, with a proportionality constant depending on the yaw angle. This turned out to be the necessary and sufficient condition to make the wall stress components normal and parallel to the leading edge also proportional in the same manner, thus reaffirming the boundary-layer independence principle for turbulent and laminar flows alike. Reinterpretation of old experiments thus changed the mantra stating, "the independence principle does not apply to turbulent flow", thus providing a new insight into three-dimensional boundary-layer flows on yawed, high-aspect-ratio wings. It explains the prevalence of attached spanwise flow near the trailing edges of such wings, and it provides a rationale for turbulence modeling on them. Furthermore, it indicates the direction along which active separation control should take place.