Of course that's a nonsense statement, based on the way things are (at least in this country) -- but I would rather be operated on by someone that had done the procedure 1,000 times before (regardless of their education) than by someone with fifteen degrees who had never done the procedure at all.
It was a joke.
But the fact of the matter is -- and left unstated -- is that communication skills are a marker for "class" and "value." So is the ability to speak in clear, non-slang laden sentences along with the ability to express abstract or complex thoughts concisely.
Following those abilities are a degree from a reputable college, the knowledge/skill set needed to buy a suit and other articles of clothing that fit and eating a meal with something approaching table manners. Less important, though related, are a passing knowledge of art, music, history and architecture.
Yes, these are shallow perceptions of people, but I have seen brilliant people languish in middle management for lack of them.