Yahoo were aware of the leak at most 45 minutes after it leaked. Damage control wasn't deployed until a day later. This is their fault. They could have nipped this in the bud by getting a decent blog post out within an hour, and contacting any news outlets who'd already run with the story.
Indeed, it is in Yahoo's interest to correct this misinformation, so I agree with your statement unironically. The press went with what it had, and if Yahoo felt like there was more to the story, it was Yahoo's responsibility to put it out there.
And Yahoo knows all this. From Yahoo's silence, I strongly believe the original story was actually correct — Yahoo intended to shut down Delicious. When the huge backlash from the leak hit, that's when the closing-Delicious story became wrong.
It may be in their interest to correct it, but it's not their obligation. Nor is it their obligation to make a web site sacred, but they did so within a day of the public making its wishes known, and likely well before they had planned to deal with the matter. I don't know what more can reasonably be expected of them.
The press was happy to read between the lines of their initial non-committal statement but not the second one where they said "ok, you win". I guess when there's blood in the water, you can't tide the sharks over with vegetables.
They are not obligated to correct it — but if they choose not to correct it, they do not have any right to complain about the circumstances that they were unwilling to change when it was in their power.
Similarly, I am not obligated to eat well, but it is poor form for me to eat Big Macs every day and then demonize McDonalds because a diet consisting solely of their swill makes me sick.