App privacy and tracking

App Store apps have a notice about the app’s privacy and tracking practices. Often it says the app will track you across sites. Yet The iPhone setting

Privacy >Tracking >Allow apps to ask to track

seemingly purports to prevent them from doing this. So the two statements are contradictory.

My question is: If my settings do not allow apps to ask to track, and I download and install an app whose App Store privacy notice says the app uses identifiers to track users across sites, can the app track me like that?