The terms psychopath and schizophrenic seem to be used in this thread with no regard for what they actually mean. Changing your mind or contradicting yourself is no guide to schizophrenia, and although this condition was only mentioned in a jestful attempt to make a point, the point seems to rely on the hopelessly inaccurate misconception that schizophrenia is a split personality disorder (as in the equally wrong joke 'Im schizophrenic and so am I').
Admitting to murder is also not good evidence for being a psychopath. Psychopaths are considered to be disproportionately responsible for violent acts, so its something you'd want to look into further, but people do violence for all sorts of other reasons too. Looking at definitions for psychopath, or more modern terms such as antisocial personality disorder, and what we actually see are a few of the symptoms that some people thought they were seeing from Amanda Knox, i.e. reports indicate that her emotional response to the killings was not what people would expect, raising suspicions.