You can always identify your customers though your application without any external library or effort. The point is that (your analytics provider) can track you through all the apps using the library. This is a significant difference, IMHO.

The developer can obviously trust themselves and the user has trusted that particular developer (and the app store approval process) as they can already use the phone features allowed to that app.

If you use Flurry/Crashlytics/... then that is an additional entity (of many people) that both the developer and the user are trusting.

Piwik allows you do not log any number of bytes of an IP address. So you can eg. make it log and display 123.213.x.x instead of a full IP. This is vastly better for privacy than sending all your visitors details to Google in the USA.

What kind of trust are you talking about?

To be fair, every server logs an IP with every request anyway.