Apple knows that I bought the app (they charged me for it).
In order to charge Clash of Clans for the conversion, my phone needs to connect to Apple and send them a record of the ad click. What if clicking on that ad and buying the app are the only thing I ever did on the phone? There’s nothing to aggregate locally, and Apple knows they got the conversion data from me.
Perhaps the claim is that my phone is going to send all these records to Apple, and Apple is just going to do the right thing and run programs that do the business without letting any of their people look at anything they aren’t supposed to look at (they could internally accomplish this by differential privacy, rigorous internal controls, etc). That’s the same claim Google and everyone else is going to make.
Even the ads can be anonymously downloaded using a shuffler/mixer, such that nobody knows which ads out of the universe of ads the device chose to target the user with.