I don't think I agree with this. It was clear as this story unfolded over the weekend that Fitz was going to lose his job. Schill had no choice. Now, if Schill had done what you suggest from the beginning, maybe he'll still have his own job in a couple months (i.e., I can't possibly imagine how this guy is going to retain the confidence of the NU faculty after this and I expect he will be fired before long too).
If Schill had written on Friday what he wrote yesterday and fired Pat from the beginning, I think that would have been a reasonable response and showed true leadership. If he wasn't prepared to make such a big decision so quickly (assuming he also just got the report), then he should have suspended Fitz indefinitely until further notice to give himself more time to sort through everything.
But by coming out with a two-week suspension as the response to what was, in the end, a pretty justifiable cause for termination two days later, it made him look like a coward who did not want to take on this burden of leadership. In fairness, this is very easy for me to say, but god-awful to have to do. I can't imagine being in his shoes on Friday. That was a shitty thing for him to a walk into so soon into his tenure. But if you are going to take on a major leadership role, then it is exactly moments like these that test your true character and your true values. Schill failed that test in my mind. If I were faculty at NU, I would want him to step down.