Kind of hard to argue since they allowed Ted Kennedy to be buried there.
The soldier qualifies to have his cremated remains placed in the columbarium, but not for a traditional ground burial.
Teddy served in WWII and those veterans are not affected to the changes in burial regulations a decade or more ago. Those changes limited traditional burials to only combat veterans. The reason is lack of space, although a few more acres have been added in the last 2-3 years.
The regulations are at: http://www.arlingtoncemetery.mil/Funeral-Information/Scheduling-a-Funeral/Establishing-Eligibility/Ground-Burial