How Important is Psychometric testing for Recruiter / HR managers when they are hiring people to see if the person is best fit for their organization?

Not much important. If a person is more smart he knows how to play.

Psychometric test proves that the person is Genuine in his answer because they ask same question in different manner and many people give different answer.

It proves that how vigilant the person is for a question asked. 

It gives a better understanding of what kind of person they are recruiting and whether he is the right candidate for the particular position

It is important because the results are measurable , as quantifying human behavior and its associated impact on the bottom line is one of the most difficult challenges facing organizations. In addition to that, Meta-analyses have shown that including psychometric assessments can improve recruitment outcomes by24% over traditional selection methods, such as resume screening and unstructured interviews.