Steve isn't blameless these kinds of things happen. The culture of secrecy he created at Apple makes rumours and speculation on areas important to the company.
There is some shared responsibility here. He doesn't have to make everything public, but he has options to crush the rumours. He could, for example, ask his doctor to submit his medical records to the SEC, so they can verify his health and release a statement. Jobs' health is a major issue for shareholders - if you want to have that much influence on other peoples' money, you have to sacrifice some privacy.