It sounds like a sensitive area in this context would be any work that involves some kind of security. It could be financial, legal, diplomatic, patenting, prototype development, intelligence, etc (intelligence not in the sense of being smart, but in the sense of gathering important information that is secret). Any area where secrecy or serious privacy is required. They would not allow another related employee to work in the same department or on the same project, because they may discuss things outside of work, likely.

A sensitive area is one where there may be financial or security risks. The firm wouldn't allow the financial manager to hire his family members or relatives as accountants or money managers in his department.