Maybe it was that Robert was using items that "should" have protected him but didn't? We know that she talked him into it by being convincing in a more mundane way, but no one else in Westeros does.
His friends and supporters (such as they are) will be more willing to believe that the Lannisters gave him shitty equipment that left him vulnerable to mind magic than that he decided death by snu-snu was a better alternative to continuing as king.
His friends and supporters (such as they are) will be more willing to believe that the Lannisters gave him shitty equipment that left him vulnerable to mind magic than that he decided death by snu-snu was a better alternative to continuing as king.