Guthrie asked Sarah Palin whether she regrets the comment. The 2008 GOP vice presidential nominee gave a terse reply and then objected to Guthrie asking the question in the first place.
"I don't regret any comment that I made, because I didn't lay PTSD on the foot of the president," said Palin, who is campaigning with Trump again on caucus day in Iowa. "You guys brought me here to talk about Iowa politics and the caucus tonight, not to talk about my kids — and that was a promise. But as things go in the world of media, you don't keep your promises."
Guthrie's co-host Matt Lauer denied that there had been any agreement not to bring up Track Palin's arrest. So we're left in a he-said-she-said situation on the promise — with no easy way to figure out what actually happened. Perhaps there was a genuine misunderstanding in which an NBC booker assured Palin that the arrest would not be the focus of the interview (it wasn't, by the way), and she took that to mean that it wouldn't come up at all. Who knows? A spokesman for the show did not immediately respond to a request for comment.
As for the broader question of fair game-ness: Sorry, Sarah Palin. It's totally in play. And there's no question about it.
Palin is the one who injected her son's arrest into the campaign by talking about it on the stump; furthermore, she politicized the issue when she used the incident to criticize the state of veterans' care under Obama. Trump, who has made caring for vets a pillar of his campaign — he staged a veterans' fundraiser instead of attending last week's GOP candidates' debate in Des Moines — has said that he suggested Palin talk about the arrest on the trail.
For similar reasons, many in the news media declared that Bill Clinton's past philandering is fair game because he is campaigning for his wife, Democratic front-runner Hillary Clinton, who is positioning herself as a champion of women. It might be personal, but it can't stay private because it's clearly relevant to issues in the campaign.
Palin said she was there to talk campaign politics. Well, guess what? Her son's arrest is campaign politics. She has only herself to blame for that.