No not bay, brown. Browns can and do have black points. Browns are also lighter around the muzzle, eyes, elbow, stifle area, and along the butt. Places that would be the last to sunfade.
Browns, and bays, are caused by agouti. Both brown and bay restrict black, but do so in different ways. Hence the reason that they can look so similar. Not all browns are super dark with lighter areas.