I have always heard the runner establishes his own "baseline", but once he establishes it he can't deviate from it to avoid a tag. Meaning, the runner can come around third, take a wide turn and then head to home several feet off of the drawn baseline...however he has to maintain that line to the plate.
In your case (and based off of what I described above....assuming it is correct), I think it would depend on the path the runner was on heading to the plate. If he had taken a wide turn and was coming from almost a 3/4 angle to the plate...then going outside the batter's box may not have been a huge deviation to warrant an out call. If he was running right down the line and then took a 90 degree turn around the batter's box and the catcher to avoid a tag...then he should probably be out.
However, I am no ump, so I am sure there are plenty on here more qualified than I am to chime in.