That argument is getting hung up on semantics. It's like saying north and south America are the same continent because they are connected. It is implicitly choosing a very specific definition of reality amongst many possible definitions.
The thing is that "personality" is a genuinely contested concept in the field (assuming that you go beyond the DSM "axes" and look at the broader debate). The semantic mess isn't merely obfuscation of established knowledge, it's also a reflection of the state of the art. From what I understand, the Big Five model [1] has the strongest empirical validation, but there are also many experts in personality psychology who regard that model as an oversimplification or even perversion of more sophisticated ideas (cf. the conflict between adherents of insight-oriented/psychodynamic versus cognitive-behavioral modes of therapy). See also [2] to get a sense of how varied the concepts are.
So screw that concept and talk about ones that are useful - ones that can allow us to make predictions. Can a person who is now bigoted and prone to violence become a Gandhi? I'd say yes, I've seen similar thing happen. Call it "personality change" or call it something else, but the phenomenon seems to be real.
