"They are stationed at a US Base and act as armed support for military missions.  But they do not meet the 330 days."

They are not enlisted, not a member of an armed forces, not military, not spouse of military? In other words, they are in a combat zone, but don't qualify for the combat zone tax exclusion. But, as a citizen:

"contractors or employees of contractors supporting the U.S. Armed Forces in designated combat zones will qualify for the foreign earned income exclusion (“FEIE”) even if their “abode” is considered to be in the United States while they are abroad."

Are you looking at the right information?