Am I correct in assuming that security during a launch rehearsal test is very high? That all the people working in the service structure have been well vetted and it is highly improbable that someone could simply walk up to the location and find a way to the white room area.
At least in the shuttle days:
To access a NASA site you must either have a NASA badge (the issuance of which required you to pass a Homeland Security Presidental Directive - 12 or equivalent background check) or be escorted by a properly badged individual. In addition to general site access, you must also be badged for the specific work areas.
To access the launch tower you must have a badge specifically granting you the privilege of entering that area. KSC was divided into a number of Controlled Access Areas (CAAs) and the areas you were allowed to enter were listed on your badge which also had your picture on it. Humorless, armed individuals prevented you from entering CAAs you were not badged for.
Here's a (slightly modified) example of a KSC badge showing access allowed to Launch Complex 39, Cape Canaveral Air Force Station, and the KSC Industrial Area. There was also a second, "portrait" oriented badge with the numerical CAA areas listed on it. This was the temporary badging issued to JSC people going to KSC for work, permanent KSC people may have had a different one. This was in addition to your regular NASA badge.