I was answering this: “Is the comparison done in my phone against a downloaded database, or is a hash of every image on my phone uploaded for comparison on a server?”

To be clear each image, the image’s NeuralHash, and a visual derivative are uploaded to iPhoto. This allows for the inspection of the NeuralHash algorithm used which I actually prefer.

The phone isn’t downloading the hash database.

From that same page: "Apple further transforms this database into an unreadable set of hashes that is securely stored on users’ devices". The phone is downloading the hash database.