I'm not really sure what this even means. Everyone has some moral right to the position they're in. The question is how much.
> He had to know this was going to happen; the last few weeks of drama have come entirely at the Lab's expense, seemingly as a long-shot gamble that Ito might weather the storm.
This is sort of the crux of my point, though. Your original argument which you seem to be backing off of is that controversy alone is a distraction, and therefore he ought to step down because he caused controversy. And the fact that he caused controversy is certainly unequivocal.
What is equivocal is whether or not he did something wrong. And that is the true issue on which the rectitude of his resignation turns. It seems to me that he probably believed he didn't do anything wrong, and as such had a moral right to retain his position because he believed he did nothing wrong. Not that anyone in a position of power should resign as soon as they cause a stir.