Cognitive Valence Theory (CVT) is a theoretical framework for exploring the give and take of intimacy between two people. As the Wikipedia article on CVT suggests, physics provides CV theorists with an analogy based on the notions of negativity and positivity, attraction and repulsion. Intimacy in dyadic human relationships occurs in a number of different ways, both verbally and nonverbally, but the nonverbal aspects far outweigh the verbal in their sheer emotional valence. Probably 90 percent or more of the affective content of communication occurs nonverbally, with the verbal aspects contributing 10 percent or less.
The author of the NYT article you quote may or may not be thinking within a CVT framework, but I wouldn't fault him or her for not citing the theory. I imagine that among the 83 people in the Practice Makes Perfect program, there is a great deal of one-on-one (i.e., dyadic) interaction between mentors and mentees, and that intimacy (of a non-sexual nature, of course) is an important aspect of what the program is attempting to accomplish.
When mentors and mentees really open up to one another, and are at least somewhat transparent with and accountable to each other, defenses tend to come down and meaningful learning can take place. In that regard, one of my favorite sayings in the art of pedagogy is "More is caught than taught," which underscores the importance of a mentor's modeling of learning behaviors and imparting not only knowledge in general to the tutee but also the tools to encourage the tutee's lifelong learning.
If you can remember vividly a teacher, professor, or mentor who made a noticeably positive and constructive difference in your life, you probably connected with that person intellectually and emotionally.