NLP is at best, seen as a pseudo-science and things of this nature have been published about its various claims in the past. It's doubtful many laymen will ever see, let alone care, about this article and what it has to say. Just reference studies that support your claims. BUT understanding the difference between using eye-cues based on ideomotor response vs. the NLP claims, there is a bit difference.
As to their claims on the Left & Right movements, that's a bit off from what I understood those positions to mean.