Earlier quoted context omitted.
It's hard to meet people like this because of attitudes like this. I have three designers on my team who are also world-class engineers, yet they often don't advertise themselves as such because they run into the "well if they do both they can't be good at either" attitude. No-one bats an eye when an engineer also turns out to be a fantastic musician, or when an engineer drives great product decisions, yet somehow be…
I would agree with you if these were complimentary skills we're talking about. However, programming and UX design are almost contradictory. For programming, you need a mathematical inclination, attention to detail, willingness to sit down and focus on one concrete task at a time, etc. For UX (and any kind of other) design, you need more an ability to create art - paint with broad strokes, look at the big picture, etc…
UX (User Experience) is about designing exactly that - an experience. It's about being extremely detail oriented, mathematical inclination (sifting through metrics, a/b testing data, CTR, bounce rates, etc.), willingness to sit down and focus on one concrete task at a time, sifting through hours of user video seeing how people interact with an application and then finding solutions to make the UX more smooth. Sound familiar to what you wrote about your "programmer"?
Not so different after all it seems.
EDIT: Everyone seems to confuse UI design with UX design. They are very different, and in some cases are different job descriptions.