Glenn Greenwald says that they do have one, and shouldn't claim objectivity in spite of that fact. It's a subject James Fallows touched on in riveting fashion back in 1996, when he recounted the occasion when an interviewer questioned Peter Jennings and Mike Wallace:
He asked Jennings to imagine that he worked for a network that had been in contact with the enemy North Kosanese government. After much pleading Jennings and his news crew got permission from the North Kosanese to enter their country and film behind the lines. Would Jennings be willing to go? Of course, he replied. Any reporter wouldand in real wars reporters from his network often had. But while Jennings and his crew were traveling with a North Kosanese unit, to visit the site of an alleged atrocity by U.S. and South Kosanese troops, they unexpectedly crossed the trail of a small group of American and South Kosanese soldiers. With Jennings in their midst the Northern soldiers set up an ambush that would let them gun down the Americans and Southerners.
What would Jennings do? Would he tell his cameramen to "Roll tape!" as the North Kosanese opened fire? What would go through his mind as he watched the North Kosanese prepare to fire? Jennings sat silent for about fifteen seconds. "Well, I guess I wouldn't," he finally said. "I am going to tell you now what I am feeling, rather than the hypothesis I drew for myself. If I were with a North Kosanese unit that came upon Americans, I think that I personally would do what I could to warn the Americans." Even if it meant losing the story? Ogletree asked. Even though it would almost certainly mean losing my life, Jennings replied. "But I do not think that I could bring myself to participate in that act. That's purely personal, and other reporters might have a different reaction."
Mike Wallace excoriated him for that answer:
"I think some other reporters would have a different reaction," he said, obviously referring to himself. "They would regard it simply as another story they were there to cover." A moment later Wallace said, "I am astonished, really." He turned toward Jennings and began to lecture him: "You're a reporter. Granted you're an American" (at least for purposes of the fictional example; Jennings has actually retained Canadian citizenship). "I'm a little bit at a loss to understand why, because you're an American, you would not have covered that story." Ogletree pushed Wallace. Didn't Jennings have some higher duty to do something other than just roll film as soldiers from his own country were being shot? "No," Wallace said flatly and immediately. "You don't have a higher duty. No. No. You're a reporter!"