Scoped storage does not prevent applications from sharing PII with each other. There are already advertising networks, using BroadcastReceivers and ContentProviders to share analytics data — it is simple and does not require individual apps to have external storage access.
However, I think you still have to hold developers responsible for clever tricks that violate the intent of the Android permissions system. There are always going to be loopholes. (This likewise means that there has to be room for developers to make honest mistakes.)
Too bad many Android developers are opposing this feature (e.g. previous discussion: https://news.ycombinator.com/item?id=19521211).