Quick question on concessions and running away.

Isn't running away a form of concession, or at least a segue into a Contest?  It capturing/killing was the point,  would probably be a Contest in the first place if there wasn't anything providing a sufficient obstacle to running.

What if the other side won't accept the concession, or if capturing them is the point?  Does that make it impossible to run away?  That doesn't seem right.

My gut instinct is to say that regardless of Concession, if you can get enough distance, it's reasonable to segue into a Contest and keep at that level - that's what "fiction first" says to me, anyway.  If capture/death wasn't the point of the Conflict in the first place, I'd still be somewhat tempted to hand out a Fate Point for the (implicit) Concession, but I'm not sure about this.

Just looking for other thoughts.