The fact that you own the KMS key doesn't stop me from reading/writing that EBS volume. It doesn't offer any additional security guarantees, especially if I was already encrypting the EBS volumes with a KMS key.
If I am a SaaS offering, whether I use a KMS key I own or one you own doesn't change the fact that I still have access to all of the unencrypted data that is silently being encrypted by those KMS keys, I've got access to the layer above it.
Sure, if the contract ended they could revoke the KMS key and now the data on the EBS volumes is no longer readable by me, but any backups I have of that data is still within my purview.