I believe it has to in order for geofenced reminders to work.
I suspect that's true and a change then with iOS 7. I can't help but think this is unintended. If this is by design, then I'd like to understand the reasoning for it.
A geofenced reminder should run in the background just like calendar, clock, phone, messages, etc run resident; and just like a reminder does when based on a time.
If I tell Siri to remind me of something when I arrive at a location and she confirms my request, then I shouldn't have to launch Reminders so that it works.