Remember, two key considerations when doing key management
1) Do not save it alongside data
2) Do not let cloud service provider manage the keys

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.

In cloud computing, the fundamental problem is that multiple organizations are now managing the identity and access management to resources, which can greatly complicate the process. For example, imagine having to provision the same user on dozens-or hundreds-of different cloud services.
Federation is the primary tool used to manage this problem, by building trust relationships between organizations and enforcing them through standards-based technologies.
Reference: CSA Security GuidelinesV.4(reproduced here for the educational purpose)

The correct order of data lifecycle is Create, Store, Use, Share, Archive, Destroy