Bill Clinton: President Doesn't "Run a Bureaucracy"

Bill Clinton recently had this to say about the role of President of the United States:

“The President is not called the Chief Executive Officer of America for nothing. You don’t run the bureaucracy but you are responsible for seeing that your ideas turn into positive changes in other people’s lives.”

Sounds sensible (although the President is explicitly called the "Executive" in the Constitution). Particularly since this guy was a President previously, and probably knows how it works. But then how do you explain Hillary Clinton's sharp criticism of Barack Obama for saying this:

"But I'm not an operating officer. Some in this debate around experience seem to think the job of the president is to go in and run some bureaucracy. Well, that's not my job. My job is to set a vision of 'here's where the bureaucracy needs to go.'"

UPDATE: Here is the audio: