I actually have a question about this.....
I've turned off BAR for all apps (the main switch), but for some reason apps still show background activity. For example, the Xbox One application shows 2 min onscreen usage and 16 mins background activity. I thought the main switch turned off BAR for all apps?
I am on 10.3.1
Again, Background App Refresh only helps apps running in the background to do so more efficiently. Turning it off does not stop apps from running in the background. Apps need to run in the background if you want them to perform well. Most don't stay in the background long. I keep all my apps on for background app refresh. No battery issues.