Runner - Out of Base Line vs Dugout

Question
Situation: Giants have bases loaded, one out. Giants' batter strikes out for second out. Giants runner on first base, thinking it was the third out, walks away from first toward dugout.  Dodgers, realizing that the Giants' first base runner is off first base, throws ball to Dodger first baseman, who only steps on first base.  Giants, realizing the runner's mistake, sends the Giants' runner back to first base.
Important Facts: While the Giants' runner roamed outside of the baseline, he did so without trying to avoid a tag.  Also, another pitch was never thrown after the strike out pitch for the second out.
Question #1: If the Giants' runner, before running back to first base, had one foot on the field of play and one foot in the Giants' dugout, is the Giants' runner safe or out?
Question #2: If the Giants' runner, before running back to first base, had both feet in the Giants' dugout, is the Giants' runner safe?

Answer
Eric,

Here's a comment from the rulebook, "Rule 7.08(a) Comment: Any runner after reaching first base who leaves the baseline heading for his dugout or his position believing that there is no further play, may be declared out if the umpire judges the act of the runner to be considered abandoning his efforts to run the bases. Even though an out is called, the ball remains in play in regard to any other runner."

To me, it doesn't matter if they make the dugout or not - if they abandon their effort to run the bases, then they should be called out.

Hope this helps!

Brian