Covering an international event such as the Olympics can be done in an almost full body cast. Unfortunately Bob Costas did not break a bone, he got a very visible affliction that impacted his face. This would be a distraction. No reputable source would let someone with such an affliction be the figurehead of their organization, much less represent them for they Olympics. It was likely just as much a decision of the networks as it was Mr. Costas. It was the right decision.
Bob Costas' did the right thing when he stepped down from covering the Olympics due to a pink eye infection. If he had a job behind the scenes I don't think it would be a valid excuse but since his job is in the public he made the right decision. As a viewer of the Olympics I really do not want to watch someone with pink eye on my television, it can be pretty gross.
I don't think it would have been very professional of him to try to cover such an important, high profile event with his eyes all swollen, red and crusty. I'm sure it would have been difficult for him to work with irritated eyes. Pink eye is also highly contagious so he did the right thing and should be commended for it.
Pink Eye is the viral infection known as conjunctivitis and is highly contagious. Costas's decision not to work ensures that he didn't spread the infection among the NBC product staff and on-camera talent as well as allowing him the time to treat his eyes with prescribed medication, eye drops and cold compresses.
No, I do not agree with his step down. Pink eye is not a very serious illness, and it could have been treated enough to go ahead and cover the sporting event. The Olympics is the biggest sporting event in the world, and he should of tried to go ahead and work.