qft and UKGuy, I wanted to respond to your comments first but think a sort of ferocious footnote about sociopathy and personality disorders would be useful now.
Personality disorders are fixed patterns of inner experience and behavior that do not change over time. Other people have quirks and flaws. For people with PDs, the whole personality is disordered. Suppose a person has depression. For as long as it lasts, the depression seems to take over the person's whole personality and life. But, take away the depression and the person is still there. With a PD, take away the disorder and there's no one there. For all practical purposes, the person is the disorder. It's the whole way he or she is configured. I'm not exploring the PD universe here - Kohut's and Kernberg's work with borderlines, the tendency of some NPDs to mellow out when they reach 50, etc. I'm explaining, albeit crudely, how people with PDs are essentially different both from normal people and people with less severe disorders.
About sociopaths in particular -- The actual diagnosis is Antisocial Personality Disorder (ASPD) and, briefly, people with ASPD are sometimes described either as sociopaths or psychopaths, depending on the extremeness of their behavior, with the former being more common and the latter being far worse and mercifully rare.
Children cannot be diagnosed with personality disorders because they are still developing. At grade school age, some will not yet display the the problems that will warrant a PD diagnosis later in life; and if there is abnormal behavior, it's too early to say whether it will or will not change. With ASPD in particular, the diagnosis cannot be made before age 15.
What about a 9 or 10 year old child who displays a persistent array of antisocial behavior; e.g., stealing, lying, damaging property, injuring others, and so on? A diagnosis of Conduct Disorder can be made.
All people diagnosed with Antisocial Personality Disorder have a past diagnosis of Conduct Disorder or a psychosocial history that meets the criteria for it even if it was not formally diagnosed at the time. The inverse is not true. Not all children who exhibit antisocial behavior grow up to be sociopaths. A child who lies, steals, and throws rocks through windows, or hits people may be reacting to a difficult home environment or to peer pressure, or to something else, and will give up the behaviors when the underlying problems are relieved.
So it's important when talking about Burke and SBP to keep the concepts and language sorted out and distinguish between behavior and personality. If he was engaged in coercive sexual behavior with JonBenet and smearing poop, then yes, that was antisocial behavior, but no, he didn't have Conduct Disorder. By all accounts, he was a nice kid, quiet, did well in school, had friends, and didn't get into trouble. Family friends and teachers might not have known what he was doing with his sister, but if he'd also been lying, nicking things from his friends, hurting people, or setting fires (and he would have been if he had Conduct Disorder), it would have come to light.
And no, although he may have had some serious antisocial behavior, he didn't have an antisocial personality. He was 9 going on 10, still developing. If he had been a little sociopath in the making, he'd have gone on to become a grown sociopath, and given his family's notoriety, we'd have heard about it -- JonBenet Brother Caught Cheating on Exams, 3rd DUI (assault charge, rape accusation, drug arrest, fraud indictment) for Brother of Slain Child Beauty Queen, Underage Sex Charge Raises New Questions About 1996 Christmas Murder Mystery. His family's money couldn't have protected him forever.
If Burke was suffering from SBP, he was acting out in reaction to severe anxiety, trauma, or abuse. The obsessive nature of the disorder could have made him capable of a premeditated sexual assault on JBR but almost certainly not premeditated murder. And, the disorder did not displace the rest of his psyche. He still loved his parents, still had feelings, empathy, needs, friends, limits and vulnerability, unlike sociopaths, who lack empathy, vulnerability, and regard for the rights, boundaries and well being of others pretty much 24/7.