Again, that's not true. Background refresh has nothing to do with whether the app is closed or suspended ("left open"). If an app enables intelligent background refresh, the OS would run the app in the background on the determined schedule regardless of whether the app is currently suspended or closed.
For example, with this new Gmail update, if you leave background refresh enabled, the app will run in the background every time you receive a Gmail push notification. It doesn't matter if the Gmail app is closed or suspended.
Most apps close automatically throughout the day even without you closing them manually. For the most part, only the last 3 or 4 apps remain suspended in memory (which does not affect battery). They OS closes them as it needs more memory for the app you are currently using.