Odd out of base path situation

Question
Odd situation in a 12U championship game and I'm not sure the correct call.  Batter hits a slow roller down first base line.  First baseman fields the ball and attempts to tag the runner.  The runner attempts to avoid the tag by running toward the outside of the basepath.  Both the runner and first baseman think the tag has been applied.  The runner stops, and the first baseman returns the ball to the pitcher.  The runner walks towards the first base dugout but doesn't leave the field of play (but was at least 10 feet out of the basepath).  Neither umpire made a call on the tag so the firstbase coach called for the runner to run to first base.  The runner did and was called safe at first (our kids were confused because they thought she was out and had walked off the field).  

I first questioned the homeplate umpire on the tag.  She said the first baseman missed the tag (although the firstbaseman and runner obviously thought she didn't).  But that's judgement so I'll go with it.

I then questioned whether the baserunner left the basepath in an attempt to avoid the tag.  The field umpire said it was her judgement that the runner stayed within the basepath when trying to avoid the tag.  Again, judgement so I'll buy that.

What I'm not sure of is whether the runner is allowed to completely leave the basepath, walk towards the dugout (obviously thinking she is out--but not completely leaving the field of play), then return to first base after the ball has been returned to the pitcher.  The umpires were clearly unsure, but allowed the runner to stay on first.  This ended up being the winning run in the championship game.

Thanks for any help you can give clarifying the call.

Answer
Hi Tim,

Confusing situation but in ASA as long as the b-r did not enter the team area or dead ball territory she would not be out and could attempt to once again advance to 1st.

No offense but w/out hearing an out call from some umpire your defense and coaches should have been more alert and finished the play either w/ a second tag or touch of the base, they had plenty of time to make sure.  Unfortunately a learning experience here.

Mark