How I understand this, for this system to work, all data on the server needs to be encrypted with the same key. If I were Alice, I think I would still be reluct

How I understand this, for this system to work, all data on the server needs to be encrypted with the same key. If I were Alice, I think I would still be reluctant to put my medical records in the cloud, if the key used to encrypt my data is shared with every other user in the system.