The scanning and matching is performed on your own device, against a copy of the databases which is encrypted to protect apple and their data providers against accountability for its content. The result of that match is itself encrypted, owing to the fact that the database is encrypted. On upload the query is decrypted and if there are above a threshold matches the decryption keys to all your content are revealed to apple.
Your phone is your most trusted agent-- it's a mandatory part of your life that mediates your interactions with friends, family, lovers, the government, your doctors, your lawyers, and your priest. You share with it secrets you would tell no other person. It's always with you, tracking your location and recording your activities. And in many cases its use is practically mandated. I think it's inappropriate for such a device to serve any interest except your own.
While it is true that the original proposal operated only on images that you would upload to icloud many people assumed the functionality would be applied more widely over time. This article seems to have proved that point: Apple is now applying essentially the same scanning technology (this time they claim the databases is of "landmarks") to otherwise entirely local photos.