In laminar flow, fluid moves in defined layers. The boundary layer closest to the wall moves with least magnitude of velocity. The direction of its velocity is the direction of flow through the tube.
In turbulent flow, molecules become disorganized and can move in eddy currents that swirl in any direction, including against each other, regardless of distance from the wall. The velocity of molecules in turbulent flow is not constrained by distance from the wall, although the link I cited says that "a general specific feature of the near-wall turbulent flows is the presence, on the wall, of a thin viscous sublayer, wherein molecular viscosity forces are dominant and the velocity distribution is linear."
Perhaps the answer you cite was trying to illustrate that neither direction nor magnitude of velocity of any one molecule in turbulent flow at the wall is predictable.