Yes, your examples are correct.

In your first example, "of Apple" implies that Apple is the one creating or imposing those standards, which makes sense - it is the "owner" of those standards. "For Apple" would imply that someone else was imposing standards to be used upon Apple. For example, you could say "Steve Job's standards for Apple." Here, a person is creating the standards that he wants to apply to the company. In the original example, though, the company itself was creating the standards.

In your second example, "for health care" is the best preposition to use, because "health care" is the object that the high standards would be directed toward / that they would be designed to achieve. "Health care" is not an entity that can create or impose the standards, but is the recipient of those standards.