(Energetics) Potential Energy and Kinetic Energy
In classical physics, kinetic energy and gravitational potential energy are almost interchangeable.  You do work on a ball and throw it vertically into the air.  Neglecting friction with the air all the kinetic energy becomes potential energy.  However, it then begins to fall, converting the potential energy back into kinetic energy.  Again, with no friction, the kinetic energy is exactly the amount that you began with.

However, we have to be careful to distinguish between ordered kinetic energy and random kinetic energy.  The ball, thrown into the air has both ordered and random kinetic energy.  The energy that becomes potential energy was the ordered form where-as the random thermal motions of all the individual atoms, which add up to no NET motion of the ball, remained the same throughout the entire flight of the ball.  

But did they?  Again and again we have to say in these situations: Ignoring friction.  Friction does in fact exist when there is air present, and friction is very relevant to this discussion.  Friction actually converts ordered kinetic energy of motion into random kinetic energy of various particles (air molecules and ball molecules).

The creation of random motion from ANY other form of energy increases entropy and reduces the amount of energy that is available to do useful work.

I'm not sure that totally answers the question.  I think that the statement needs to clarify that random motion and its associated kinetic energy is, as your note claims, a preferred state over potential energy.