I don't know how apple manages it but the new testflight is a pain to use.
The process of adding a tester alone is not intuitive and requires way too many steps.
I switched to installrapp.com for testing iOS stuff because I don't have the time to spend on finding out why the app I released for testing is not showing up in my clients test flight.
I've been using Beta by Crashlytics as it is nice and cross-platform and works with ios7. Downside is the integration process and management console are a little tricky.
Crashlytics (now owned by Twitter and rebranded as 'Fabric') is great. I'm surprised you thought the integration was tricky as it's the most simple setup I've seen. You install a menu bar app that literally walks you through each step and which automatically grabs your archives (when you archive a build) and lets you send it to testers in a couple of clicks.
The process of adding a tester alone is not intuitive and requires way too many steps.
I switched to installrapp.com for testing iOS stuff because I don't have the time to spend on finding out why the app I released for testing is not showing up in my clients test flight.