That is all correct, of course. The relevant part is
(b) while engaged in military operations involving conflict with an opposing foreign force;
which pretty much opens it wide to cover just about anything.
Traditionally, the Bronze Star was reserved for forces that were actually involved in combat operations, not the support units. Support, including staff, have another set of roughly equivelant awards that rank just below the comparable combat awards.
For example, I have two DMSM's and an MSM which are the "staff equivelant" of the Bronze Star and rank just below (appropriately). Up until the current conflict, those were what were handed out to forces not engaged in direct combat. To hand out Bronze Stars to staff pukes and service support forces "inside the wire" violates a very long tradition.