I have no problem with people/companies calling something a mistake where another would put PR fluff. At least it implies that your users/customers have legitimate standards other than "take it and like it."
As to not admitting it was a mistake... I'm saying you don't apologize for the DickBar. It didn't work, learn something from it, and move on. But clearly, Twitter was far too short-sighted that they didn't even have a backup plan, or competing ideas as simple as... "what would happen if we instead moved the ads to the bottom?" AdMob already bombards many users this way. Would that work?
And as mentioned, I don't have a problem with companies apologizing if they royally screwed up--I mentioned two specific cases where it was warranted. But apologizing every time someone with a blog ridicules a feature/ad model? Not a good sign.
http://en.wikipedia.org/wiki/Eating_your_own_dog_food
It seems you meaning not admitting mistakes/showing weakness. I agree companies should admit mistakes in the present era.
I think we'd all like to think that people at Twitter are the cutting edge of whatever, Web Scale, but the people who work there are in a bubble of what they're told just as much as people at other companies. When you're in the middle of an industry it's hard to be objective, increasing the odds that something like this would be thought of as a good idea. So whatever, now Twitter's got their own Microsoft Bob. At least it's dead AFAICT.