If heat energy added to a system can be stored as kinetic energy of the particles, that means that, if the system has heat energy, the particles will have kinetic energy. It's as simple as - the particles are moving, and therefore they have kinetic energy. Also, the potential energy being referenced is most likely not a reference to atomic energy; it is probably to do with phase or some other physical arrangement (but that is off topic).
If you really want to say that moving particles don't have kinetic energy, that's fine, but every physicist I've ever met (including all the ones I worked with at FNAL) will completely disagree with you.