Density and damping
The "fly low" advice comes because damping is affected by altitude, particularly in yaw. Put in very simple terms, the yaw damping comes from the vertical stabiliser moving sideways through the air as the tail yaws from side to side. The denser the air is, the more damping there is, which means the yaw oscillations will die out quicker.
The rolling motion in a dutch roll comes from sideslip oscillations, which are an inevitable consequence of yaw oscillations. Again, roll is damped more by increasing density because the wings moving up and down during a roll have more air molecules to react against. This is particularly important for swept wing aircraft, which tend to have high lateral stability and thus roll a great deal with relatively little sideslip present.