I think we can say a couple things about this episode.
The first is that Trump is asking for special treatment simply by virtue of who she is. There is no other way to read it. If she were any other presidential adviser, the question would not have seemed out of bounds to anybody. By installing his daughter and her husband in high-ranking positions in the White House, President Trump has created this uneasy balance — both for his advisers/family and for the media.
It's also hugely important to note that the interview was conducted while Ivanka Trump was on official business at the Olympics in South Korea — during a trip, no less, in which the White House emphasised that she was acting as a diplomat rather than a daughter. the Washington Post's Jenna Johnson sums it up well:
But the second — and I would argue more important — point is that there are just so many unanswered questions here, which makes the question fair game. Trump would probably argue that she was singled out for this question because she is the president's daughter in addition to being an adviser. But the staff who have been asked about the allegations haven't exactly provided many answers.
The president's personal lawyer, Michael Cohen, has confirmed that he was behind that $130,000 payment to porn star Stormy Daniels. But he only confirmed it in the face of a campaign finance complaint against him — after he offered vague denials about the whole thing. And Cohen's apparently carefully phrased statement about the matter also led to plenty of questions that he has said he will not answer.
The White House also has been silent on this from the briefing room podium. Deputy press secretary Raj Shah was pressed on Thursday on the matter but wouldn't commit to getting any answers:
Q: Last week, the president's personal lawyer acknowledged giving a $130,000 payment to Stormy Daniels. Is the president aware that his lawyer paid that kind of money to a porn star to buy her silence? Does he approve of that?
SHAH: I haven't asked him about it, but that matter has been asked and answered in the past.
Q: No, not since he acknowledged this. He acknowledged this last week. This is the first time we've had a chance to ask about it. So can you go back — can we find out if the president approves of the fact that his personal —
SHAH: I haven't asked him about that.
Q: Will you ask him about that?
SHAH: I haven't asked him about it.
Q: But will you ask him about it, Raj?
SHAH: I'll get back to you.
The president has also been unusually silent about this whole thing. Despite calling women who accused him of sexual harassment "liars" in the past, Trump has been quieter about allegations from Daniels and Playboy Playmate Karen McDougal. Even in a New Yorker story on McDougal, a White House spokesman offered an odd statement that attributed the denial directly to Trump — rather than simply denying it. Likewise, Trump's previous denials have been filtered through Cohen, who originally said of the alleged Daniels affair: "President Trump once again vehemently denies any such occurrence, as has Ms. Daniels."
The whole thing is just weird. There are so many unanswered questions, not least of which is whether Trump had any knowledge of or involvement in the payments. And the people who are tasked with answering those questions haven't done so. So when NBC has a sit-down with presidential adviser Ivanka Trump, you can understand why they'd want to ask.