I don't think we are in any disagreement that whoever is uploading the data "owns" the data. The interesting idea is that the entity storing the bytes has 0 information about the data they represent, in the information theoretic sense, since they can decrypt the data to any value by choosing a sufficient key.
This is not true for most other encryption schemes where the encrypted data has enough structure to it that theoretically it could be retrieved without the key, although the whole point of the encryption is that this isn't a practical undertaking.
I don’t actually store child porn - the videos I have are all decryption keys to files filled with zeros that I have encrypted with a one-time-pad cypher.