It is true. This is how Private cloud is defined.
Private Cloud: The cloud infrastructure is operated solely for a single organization. It may be managed by the organization or by a third party and may be located on-premises or off-premises.

They are considered as forms of data breached and require notification. Further cloud customer is legally liable.

The CSA STAR Certification is a rigorous third-party independent assessment of the security of a cloud service provider. The technology-neutral certification leverages the requirements of the ISO/IEC
27001:2013 management system standard together with the CSA Cloud Controls Matrix.

Cloud computing changes the responsibilities and mechanisms for implementing and managing governance. Responsibilities and mechanisms for governance are defined in the contract. as with any business relationship. If the area of concern isnt in the contract. there are no mechanisms available to enforce. and there is a governance gap. Governance gaps dont necessarily exclude using the provider, but they do require the customer to adjust their own processes to close the gaps or accept the associated risks.
Ref: Security Guidance v4.0 Copyright2017, Cloud Security Alliance (used for educational purpose here)

Definitions:
Due diligence is the act of investigating and understanding the risks a company faces.
Due care is the development and implementation of policies and procedures to aid in protecting the company, its assets, and its people from threats