We're programmers/engineers, not painters/artists. Hence I don't see where that statement doesn't hold absolutely true for us. (Except perhaps for management, team leads and entrepreneurs.)
Have a quick look at new pursuits such as:
http://www.engineering.cornell.edu/magazine/features/empathy...
https://phys.org/news/2015-11-empathy-faculty.html
I could discuss this at length because it's a subject that really interests me, and I'm severely biased because I started out in the humanities with my main pursuit being an understanding of the human condition. I've brought those learnings with me into my current software engineering career and it's serving me well.
Simple being able to place yourself in the shoes of an end user, rather than dictating to them what they necessarily have to learn (and even better, when you know they should learn something with improved understanding of how to implement such a feature) saves everybody a lot of time and frustration. Your estimates will improve in accuracy as well. You'll see less scope-creep.
It's especially important in critical-systems work.
Plus I consider it a bit of a boon to someones character if they care about what they're putting into the world. Most people do. Hint: it won't inhibit your technical understanding.
(But each manager or lead usually has more than one report, so there are likely very few managers/leads compared to everyone else. Hence the general sentiment.)
What we need more in this discussion is more emotional intelligence, not less.