Under most circumstances, police officers on military are "civilian" employees rather than military police. {And I "..." civilian because most police officers refer to the likes of us as civilians.} This is because, in a military context, law enforcement is just not a military function. The US military moved away from having soldiers function in non-military roles (such as, to give another example, the time-honored KP) many years ago. There are exceptions, of course (I got a speeding ticket from a (female) MP sergeant on Ft. Bliss a couple of years ago).

Since soldiers of any rank are not allowed to carry weapons on duty, unless they are heading for the firing range, and carrying of privately-owned weapons off duty in not allowed on military installations, it is most likely that any armed officer responding at Ft. Hood was a civilian police officer rather than a "regular American Army white person". In fact, one officer was (visually) African-American and the other was (visually) a "white" female.