Some politicians are impeccable; if you ask them thorny questions like scandals, they always throw out a new question to change the topic.
This interviewer didn't let it go: https://www.youtube.com/watch?v=pyqnu6ywhR4
Often they will just talk around a question too. They will be asked if they will give everyone free ice cream if elected, and they will just talk about how great ice cream is, how important ice cream is, etc, but never actually answer the question.
I'm surprised there isn't a term for doing that.
This is a basic survival skill in politics, and not just for scandals.
Let's take Bernie Sanders, because he's well-known in Vermont for being happy to go off-script and actually talk to people. During my only personal conversation with him, he was delighted to discover that a small, local event actually served excellent chicken. (Apparently politicians eat a lot of rubbery chicken.)
But at that same event, Bernie was approached by a woman asking some conspiracy-tinged question. And he very gracefully deflected and changed the topic. I think that just about anyone who interacts with the public is likely to pick up some version of this skill eventually.
I don't think anyone is born like that. Politicians are trained for it. I remember a podcast where they talked about Al Franken and how it was difficult to get him to stop answering questions. The goal: one, maybe two or three talking points at any given time and no matter what question anyone asks, it is your job as a politician to give a non answer and pivot to the point of the day.