I understand you point here, and yet I do wonder whether Giuliani himself is on speaking terms with former officials of the Giuliani administration.
But I'm willing to be persuaded. Whom would you suggest?
One of the rules of good journalism is "if your mother says she loves, you, check it out." If the New York Times were a good newspaper, and some guy says "I had a nervous breakdown because of what Giuliani did to me" I would call the heads of the agency that made the decision against the guy. Why did they say they did it?
After printing both sides' explanations, the next step is to find any relevant facts that may influence the argument. Let's say person A says "I was fired because I stood up to the administration" and person B says "Not true. We had to let everyone go with less than two years of experience because of budget cuts." The reporter should then see if everyone with less than two years of experience really was fired. The resolution of that question will make one side's argument look better than the other side's, but that's not bias--only reporting the facts.
The next step would be to provide some context. One of the shoddiest articles I ever read was trying to make the case that nearby military testing in the town where I grew up was causing increased rates of cancer. The article claimed "this town had a higher rate of cancer than what would be expected." Any decent journalist would have asked a few experts and noted that the town in question was a farming community at high altitude, and thus had a high rate of skin cancer. They didn't consider the larger picture that cancer rates vary from place to place.
Anyway, the New York Times in this case neither provided the opposing arguments nor gave many supporting facts nor provided context. It's not the way a real newspaper would behave.