Eh, it's sort of correct.
https://en.wikipedia.org/wiki/Nimitz-class_aircraft_carrier
This manning seems to include the airwings though, which aren't permanently attached to the ships, so not really considered part of ship's assigned crew unless they are basically out to sea with us.
The biggest issue truly is certain critical rates (several of which are crucial to the operation of an aircraft carrier) that are hard to man even in bad economic times, due to the stringent qualifications and training these jobs require (usually highly intellectual in nature). Some require things like "at least a B in an Algebra class". Sailors usually need a high ASVAB score (80+ for several jobs), which means that only the top 20% of those who apply for the Navy would even be eligible to start the schools. Other things will disqualify Sailors from these schools too, such as age, many mental health issues (which would not be an issue for other ratings), history of any suicide attempts or thoughts, or even integrity issues. Bonuses are a clue that a rating is undermanned. And there are several that get 5, even 6 digit reenlistment bonuses.