The moderator in Tuesday night's presidential debate, after appearing to side with President Obama on the question of whether he called the Libya strike a terror attack from the start, conceded afterward that Mitt Romney was "right" on the broader point -- that the administration for days insisted it was a spontaneous act.

"He was right in the main. I just think he picked the wrong word," Candy Crowley said of Romney on CNN shortly after the debate ended.

Crowley was referring to the tense exchange in the final half-hour of the debate, when Romney questioned whether Obama had called the attack an "act of terror" rather than "spontaneous" violence that grew out of a protest against an anti-Islam video.

Crowley then intervened. Here's the exchange:

ROMNEY: I think (it's) interesting the president just said something which -- which is that on the day after the attack he went into the Rose Garden and said that this was an act of terror.

OBAMA: That's what I said.

ROMNEY: You said in the Rose Garden the day after the attack, it was an act of terror. It was not a spontaneous demonstration, is that what you're saying?

OBAMA: Please proceed governor.

ROMNEY: I want to make sure we get that for the record because it took the president 14 days before he called the attack in Benghazi an act of terror.

OBAMA: Get the transcript.

CROWLEY: It -- it -- it -- he did in fact, sir ... call it an act of terror.

Click for the full debate transcript.

Obama, indicating he thought he had just gotten a boost from the moderator, then chimed in: "Can you say that a little louder, Candy?"

However, Obama didn't explicitly label the Benghazi strike terrorism in those Sept. 12 remarks. What he did say is: "No acts of terror will ever shake the resolve of this great nation."

Crowley, during and following the debate, pointed out that despite Obama's Sept. 12 remarks his administration was peddling a different story to the public. She said it took two weeks for officials to say more definitively that the attack was more than an out-of-control protest.

And she continued to clarify on CNN that Romney was making a legitimate point.

"Right after that I did turn around and say, 'but you are totally correct that they spent two weeks telling us that this was about a tape'," she said.

Click for the full Rose Garden transcript.

Four days after Obama's Rose Garden remarks, Susan Rice, the U.S. ambassador to the U.N., went on five networks' Sunday shows and cast the attack as hardly a coordinated strike by terrorists.

"We are obviously investigating this very closely. The FBI has a lead in this investigation," Rice said Sept. 16 on "Fox News Sunday." "The information, the best information and the best assessment we have today is that in fact this was not a preplanned, premeditated attack. That what happened initially was that it was a spontaneous reaction to what had just transpired in Cairo as a consequence of the video. People gathered outside the embassy and then it grew very violent and those with extremist ties joined the fray and came with heavy weapons, which unfortunately are quite common in post-revolutionary Libya and that then spun out of control.

"But we don't see at this point signs this was a coordinated plan, premeditated attack. Obviously, we will wait for the results of the investigation and we don't want to jump to conclusions before then. But I do think it's important for the American people to know our best current assessment."

Click for the full 'Fox News Sunday' transcript and video.

State Department spokeswoman Victoria Nuland, White House Press Secretary Jay Carney and other administration officials did little to discredit that assessment until Sept. 19, when Matt Olsen, director of the National Counterterrorism Center, testified at a Senate hearing.

"Yes, they were killed in the course of a terrorist attack on our embassy," Olsen said.

Even so, Obama taped an interview on ABC's "The View" on Sept. 24, nearly two weeks after the attack, in which he declined to label the attack terrorism when asked. Instead, he would only go as far as to say the attack "wasn't just a mob action."

After the debate Tuesday, Obama tried to clarify his remarks. The man who posed the Libya question, Kerry Ladka, told Fox News that the president approached him after the debate to explain he delayed explicitly labeling the attack terror because "he really wanted to take the time to be deliberate, to make sure he had all the information."

There were several more factual slips during Tuesday's debate.

-- At one point, Obama repeatedly said "not true" when Romney claimed oil and gas leases and permits were down by half on federal property.

Romney was exaggerating a bit. But Obama also dismissed an overall trend that is demonstrated by the numbers. According to Bureau of Land Management figures, the number of new leases fell by roughly 42 percent in Obama's first three years in office, compared with the number in the last three years of the George W. Bush administration.

-- Romney, meanwhile, tried to assert that the price of gas should be the barometer for whether an energy policy is succeeding.

"The proof of whether (an energy) strategy is working or not is what the price is that you're paying at the pump. If you're paying less than you paid a year or two ago, why, then, the strategy is working. But you're paying more," Romney said.

However, global markets play a big role in setting the price of oil. Demand in the developing world likely would be a far bigger factor in determining that price than the U.S. president's domestic drilling platform.

-- Obama also claimed Romney said on "60 Minutes" that it was "fair" for somebody making $20 million a year to pay less in taxes than a nurse or bus driver.

Romney's statement, though, in that interview was broader than that. Romney said, when asked whether it's fair for investment income to be taxed less than the income of someone making $50,000 a year: "Yeah, I think that's the right way to encourage economic growth, to get people to invest, to start businesses, to put people to work."