Take whatever you find with a grain of salt. A lot of people--especially journalists--either don't understand or won't report details on which branches of government has what responsibilities. For instance, the president cannot send in the military unless a) requested to do so by the governor or b) he declares martial law. Also, the mayor does not control the National Guard--the governor does.
In reality, the rules are somewhat blurred. There is currently a military presence in New Orleans, although neither of the two conditions mentioned above have occurred.
It's not like a big corporation with a CEO and a bunch of VPs and a bigger bunch of directors. The mayor does not report to the governor and the governor does not report to the president. It's more akin to alot of different corporations--some large, some small--all competing and occasionally cooperating with each other. Although that's really not the best analogy, either.