The Pentagon has it's own airport, directly north of the facility, called the Pentagon ahp.
Shortly to the east-southeast, directly across the Jefferson Davis Highway, is Washington Airport, a public international airport. Does that not impact your assertion that a Pentagon employee would almost certainly be on any given morning flight out of Dulles? For most, wouldn't Dulles be 22 miles out of their way?
Ronald Reagan Washington National has perimeter restrictions as outlined in the following:
Government employees are limited to flying contract carriers. These carriers change throughout the year. Contractors (I used to work for a defense contractor based in the DC area). are usually required to fly cheaply. Both sets can retain their frequent flyer miles for personal use and thus try to fly the same carrier. The government employee can't always do this because of the requirement to fly contract carriers.
As I was based in the DC area and flew to the west coast a lot (50k miles a year) I would fly mostly out of Dulles but sometimes out of Baltimore as the flight could be significantly cheaper. I have flown on the same plane as my companies CEO (who was famous in the company for not having a private jet) many fellow staff members of company and program office (i.e. government personnel). Don't forget a direct flight is not the same as non-stop. Most of the time I used Dulles even though it was a longer distance from where I lived than DCA because the overall travel time was less or it was cheaper.