I've never tried it but I saw this a while back. By looking at it, it seems like it will help your case but unfortunately, you gotta give it a try to find out if its worth it or not.
https://developer.apple.com/downloads/index.action Go to that website, and login using your developer account. Go to page 2 (or find Oct 4, 2013 post Bug Reporter Logging Profiles (iOS)). In the description, Apple has a link that tells you how to use these profiles. As the title of that post suggest that it is used for bug reporting, hopefully it gives you some details so you could fix your bugs.
Try it and see if it works and let other people know if it's useful or not. Since it says 'Logging', my guess is that it will output detail info on the console about push messages and not secretly log and sends the log to apple.