@Keith @Shaaz @Anindya: thanks for the question and explanations.
Assuming I understand right then, this is just different terminology for the fundamental difference between a preorder and a poset. At least, using the common meaning for those things outside the book. Specifically:
* A poset must obey antisymmetry (= "skeletality").
* That's what differentiates posets from preorders.
Stated alternately, it's antisymmetry that prevents non-trivial cycles.
Is that correct? Thanks.