The BEST indication that an organization has a mature information security culture is when its staff consistently consider risk in making decisions. When an organization's staff understands the risks associated with their actions and are empowered to make risk-informed decisions, it indicates that the organization has a mature information security culture.
According to the Certified Information Security Manager (CISM) Study Manual, "A mature information security culture exists when the people within the organization understand and appreciate the risks associated with information and technology and when they take steps to manage those risks on a daily basis." While information security training, documented information security policies, and regular interaction between the chief information security officer (CISO) and the board are all important components of a mature information security culture, they are not sufficient on their own. It is only when staff consistently consider risk in making decisions that an organization's information security culture can be considered mature.
Reference:
Certified Information Security Manager (CISM) Study Manual, 15th Edition, Pages 151-152.

The best way to address this situation is to assign responsibility to the database administrator (DBA). The DBA should review the databases for sensitive content and assign the appropriate classification level to each database. This should be done in accordance with the organization's information security policies, which should outline the rules and guidelines for classifying information assets. Additionally, the information security manager should prepare a report of the databases for senior management, noting the databases that do not have owners assigned to them, as well as any other relevant information. This will help to ensure that the organization is properly managing its information assets and that any risks associated with the lack of owners are identified and addressed. This information can be found in the ISACA's Certified Information Security Manager (CISM) Study Manual, Section 5.3.

The explanation given in the manual is:
The information security manager's knowledge of the business is the most critical factor for information security program success because it enables him or her to align security objectives with business goals and communicate effectively with senior management and other stakeholders. The other choices are important elements of an information security program but not as critical as the information security manager's knowledge of the business.
An information security program is a set of policies, procedures, standards, guidelines, and tools that aim to protect an organization's information assets from threats and ensure compliance with laws and regulations. An information security manager is a professional who oversees and coordinates the implementation and maintenance of an information security program. An information security manager should have a good understanding of the business environment, culture, strategy, processes, and needs of an organization to ensure that security supports its objectives.