I think you may be splitting hairs here, but I think you're referring to this information from the above referenced document.
"Instead of scanning images in the cloud, the system performs on-device matching using a database of known CSAM image hashes provided by NCMEC and other child-safety organizations. Apple further transforms this database into an unreadable set of hashes, which is securely stored on users’ devices." (page 4)
Just a little bit further down on that page:
"Before an image is stored in iCloud Photos, an on-device matching process is performed for that image against th database of known CSAM hashes. This matching process is powered by a cryptographic technology called private set intersection, which determines whether there is a match without revealing the result. The device creates a cryptographic safety voucher that encodes the match result. It also encrypts the image’s NeuralHash and a visual derivative. This voucher is uploaded to iCloud Photos along with the image.
Using another technology called threshold secret sharing, the system ensures that the contents of the safety vouchers cannot be interpreted by Apple unless the iCloud Photos account crosses a threshold of known CSAM content. Only when the threshold is exceeded does the cryptographic technology allow Apple to interpret the contents of the safety vouchers associated with the matching CSAM images."
So, while the hashes are present on an iOS 15+ device, no matching/scanning is done unless the photo is uploaded to iCloud Photo Library.
Thank you for finding that as I was trying to dig it up myself again.
Maybe I am splitting hairs, but I still see no verbiage that states the matching/scanning does not happen if iCloud Photos is disabled. Nothing happens with that match until it is uploaded to iCloud Photos, but nothing clearly states the match does not happen if it is disabled.