"It's not true. It's not true. It's not true.

"...

"It's old news."

I'm loosely quoting a source I can't remember, but I think it was ridiculing a repeated tactic of some candidate. It's a dynamic that seems to play out a lot if you know to look for it in issues that involve a lot of public relations games.

I think you are right to emphasize how little we remember when we learned what. That's why the above tactic works so well. It lets politicians' dance around their tactical mistakes and change positions without undermining their own base. It is also how disingenuous people can now able to talk about "welcoming debate" and have a large portion of the population perceive this as advocating some reasonable middle ground.