The only apps I have set to background allowed (other than the ones that cannot be changed) are WPCentral, Cortana, Bing Weather, OneDrive, Calendar, Store, Here Drive, and Skype. A few of those are pretty necessary for functionality I require (live tiles, notifications, backup of pictures).
The Battery Saver individual app usage reporting doesn't give me any insight as to a specific app that is going nuts in the background, but I really don't think it reports very accurately either. Whichever app I use the most, that one is always tops in the list even if it shouldn't use a lot of battery (I can see games burning through battery, but not something like text messaging).
But as chezm mentioned, seems like a lot of people getting good battery life don't need to sacrifice functionality. Seems more random than anything.