How to get Mail in iOS 7 to automatically clear unread email badge

I thought that the whole new background app refresh in iOS 7 would help this issue.....

I like that I can look at my iPhone 5s running iOS 7.0.2 and see that I have unread emails from the red badge on Mail

However, if I do not use the iPhone to read those emails and I instead use my iMac, I thought that the badges on the Mail icon on the iPhone would automatically clear with the combo of using the push server an background app refresh.

However, even if I read emails on my iMac, the Mail badge on the iPhone will not clear unless I launch Mail on he iPhone.

FB badges go away if I check FB on the computer.

Why not Mail?

And is there any way to fix this?