If WYOTECH and EVEREST sending recruiters to the bases to sign up students, they MUST be requesting access EACH TIME through the Education Center, if they are following protocol. They must also be stating on the request the reason they are on post (this is the way the Army does it; other Services have different methods).
There is generally a time and space limit for school officials. The installation access is very specific about what the visit is for, how long it will be and where it will be conducted. If an official is outside of the scope of the request, for example, is supposed to be in an office in the Ed Center but is seen at the Library putting out brochures, then that is a violation that is reportable. My understanding is that under no circumstance are they supposed to put out literature (or have any agent do so) that hasn't been seen/approved by the ESO.