Final answer:
A centralized administration approach provides strong control to headquarters, so it's false that it would offer only moderate control.
Step-by-step explanation:
A centralized administration approach implies that the main headquarters of an organization has substantial control over decision-making processes and administrative tasks. This suggests that headquarters would have a significant level of authority and influence in directing research, managing funds, and maintaining oversight on various operational aspects of the organization. Therefore, the statement that a centralized research administrative approach offers moderate control to headquarters would be false, as such an approach typically implies more than moderate control, leaning instead towards a high level of central control.