Final answer:
The most appropriate authentication method that meets all the specified criteria is a complex passcode. It is non-invasive, adds a second layer of security, does not share personal information, and has a low false acceptance rate.
Step-by-step explanation:
The best authentication method for the secure facility's server room that meets the criteria of being non-invasive, a second factor, not sharing information, and having a low false acceptance rate is D. Complex passcode. A complex passcode does not require any invasive biometric scans such as fingerprint or facial recognition, which makes it non-invasive.
As a second factor, it adds an additional layer of security beyond the physical key without requiring any biometric data that could be considered invasive or sharing personal information. Complex passcodes also provide a high level of security with a low false acceptance rate, ensuring that unauthorized individuals are unlikely to guess or replicate the passcode.