Some additional observations/opinions FWTW:
I observed Our Leader from a distance of about 30 feet perform all the appropriate tasks of a Chairman at the Annual Meeting of Shareholders in Cupertino . . . for probably close to 2 hours. Date: March 4. He appeared trim/slender/vigorous enough for a man of 50+. Importantly, he displayed his usual in-control demeanor. No question who the boss is, however he did have at least 2 other execs with him, on-stage, perched on the trademark stools, throughout. in 2006 and 07 there was only 1 other exec at a time sharing the small stage. He is not afraid to share the reporting duties, though having some familiarity with Annual Meetings, the reporting is always well rehearsed. Apple's planned and the spontaneous portions, alike, were slick as greased glass.
SPJ handled (est) 90 percent of the shareholder queries . . . with aplomb. and no small measure of wry humor . . . including a serious question about his recovery from surgery and Apple's succession planning (post-Jobs).
(I'm acquainted with his Doc at Stanford - arguably the best in the world w/respect to the pancreas.)
"Material events" in a corporation's management (e.g. changes) are absolutely required to be reported publicly, as has been mentioned here. Death, kidnapping, resignation, termination, leave of absence seem well-understood as material events. General health remains a gray area, by definition.
I really would doubt that Apple will "toy" with public information. However, they, as are other corporations, are somewhat helpless in the face of false or malevolent rumors. (Check the evening news . . . any day!
I believe him when he says they have worked diligently to design and develop a sound succession plan.