@blatham,
I would say that those would be exaggerated overstatements, but based indeed on some of Trump's observable behavior. There's certainly a great deal of self-reinforcing rhetoric and speculation out there on these and related topics.
I have learned to base such judgments mostly on what people actually choose to do when confronting serious matters, as opposed to extrapolations based on relatively superficial mannerisms and spontaneous behaviors.
Certainly Trump has endured in a situation involving weighty responsibilities, while beset with constant, often irrational and vicious opposition and criticism from media and political opponents, to a degree and intensity not seen here in a century. That itself could be an indicator of a very secure and stable personality. He has pursued the goals and priorities he articulated in his campaign with degrees of intensity and actual success, only rarely seen in American politics, and has done so in the face of constant attacks on his policies (that's OK), and also his person and his family - challenges his predecessors didn't face to nearly the same degree.