Pay out of pocket for PCS?

Hello. Hoping for a JTR guru to help me understand something. I have an upcoming PCS CONUS to OCONUS. My spouse and I are going. Our plan is to go on leave prior to departing. This way we can spend time with family before being out of the country for 3 years.

The problem is that my local travel office is insisting that they can only book our flight on a government rate if we depart from our current duty station, and if we depart from another location they can't use a government rate and I have to pay the difference (which adds up to about $800).

Now, I could understand if it were more expensive to fly from my leave location to my new duty station, but the flight (on a GSA rate) is $120 LESS per person if we fly from the leave location.

So, to make sure I understand, we're not allowed to book a LESS expensive flight and save the military hundreds of dollars because it's from a different location than where I'm currently stationed?