If the decision has been made to go public (or attempt to do so), that disclosure would likely be required. However, repurchases that are being done with a view to possibly making going private easier in the future, should the company decide to do so, wouldn't trigger a disclosure requirement. That being said, the possibility of Disney planning (or even considering) going private without a new investor putting up huge money is almost inconceivable. Dell had Michael Dell. Disney has no such large owner.
Wrong. There are two main reasons that companies repurchase stock. First, because they believe that the market is undervaluing the company and therefore buying its own stock is a good investment. While you could describe that as "supporting the stock price", that would be an inordinately pejorative way of describing it. Second reason is because the Company has decided it wants to return cash to shareholders, and chooses to do it via stock repurchases rather than a dividend. I find repurchases to be a more efficient means of returning cash shareholders, as it allows shareholders to decide whether to turn in all or a portion of their holdings for cash, rather than requiring them to do so, as a dividend would.
The execs are no doubt tired of some of Wall Street's tendencies. But the access to cheap financing overwhelms all of that. And the math makes it easy to see why. With a market cap of $163 billion, every 1/100th of a percentage point less that the market demands as a return on investment implicitly saves the company $16.3 million per year.
Disney used to print out their stock certificates on better paper. Also, you can't buy candy and the like with them at our local convenience store, so one has to surmise the certificates are worthless.