I definitely think there are certain people who are born with negotiation skills, and those that are not. You can always get better of course, but some people have a natural ability (a specific form of empathy) to know what exactly the other party is thinking, feeling, and expecting, and can exploit it as much as possible. Its just as much a skill as a talent, and can be used for both good and evil.
According to what I've seen and read, there is no special talent to knowing what another side is thinking. It's just good listening, not assuming anything, and asking lots of questions. People who don't do these things will rely on guessing to understand the other side and will often be wrong.
