The Cloud Security Alliance STAR Registry is an assurance program and documentation registry or cloud provider assessments based on the CSA Cloud Controls Matrix and Consensus Assessments Initiative Questionnaire. Some providers also disclose documentation for additional certifications and assessments(including self-assessments).
Ref: Security Guidance v4.0 Copyright2017, Cloud Security Alliance(used for educational purpose here)

This is true, When cloud assessment is done, it is very important to understand the scope of the audit and the standard used. In statement above, we can see that, audit scope ofSSAE16 is decided by cloud provider and can be very limited and one may not be get full visilibility into the security of the cloud service provider.

Even after cloud migration. cloud customer is responsible for the data and ultimately liable for any data loss or breaches.