its possible, most dogs will make a big show of themselves and 90% of the times cannot back it up and will flight if the charade doesn't work (or fight if they are at home or close to home - as they leave that circle that is "home" they'll be less and less likely to fight and more likely to flight - but a huge part of that is also personality). So its possible that what you did not see what Kira showing dominance, the other dog not impressed, and what you did see was the other dog pursuing Kira and Kira hitting fight or flight and choosing flight.
So, its possible that you missed the signals that Kira was giving up and only noticed the actions that followed (which were much less subtle).
Why do I keep saying "its possible"? Because without seeing it, we have no idea what could have triggered it or what could have happened. It's all just grasping at straws at this time.
When all else fails, and you analyzed every possible scenario and cannot come up with a consistent reason for the action you are analyzing, just remember: dogs are weird
by the way, are we still hitting that trail tomorrow morning? could be fun, but I'm not sure how early you usually get up. I can't stay in bed past 7:30AM because of the constant staring (you know by who hehe)