Being not-so-nice can definitely be a symptom of playing well with others. The stereotype of the "popular" kids in high school is that they're jerks. And yet, they're considered the ones with the best social skills!
It's a fine line between 'social skills' (playing well with others) and 'manipulation' (getting others to do what you want them to).
Many people that are very successful are really good at getting others to do what they want them to do by pushing the right buttons. That does not make them 'nice people' or 'people that play nice with others'.
