In the advice context of the article, the goal is (for an arbitrary person) to be successful and liked by an audience (whether the TED audience, or an audience of employees, or an audience of TV viewers, or in front of friends and acquaintances). In that context, I'd say being authentic doesn't make you likable, but if you can be authentic while simultaneously being likable, people love that.
Brutal honesty, which is a different thing, will not win you friends. No one likes the person who says, "What? I was just being honest!" Social interactions are transactional and layered with meaning. "I want to have sex with you right now" is not merely a random act of stating a fact, and neither is a personal criticism (e.g. "you're ugly"). An exec who asks her employees for emotional support is making an ask that may not be comfortable.
My advice is to learn to be more authentic (with fewer self-inhibiting inner dictates), for your own personal reasons, and simultaneously to learn how to better relate to other people.