Runner is out when he leaves the field of play -- or not?

[Alaska Ump]

Adult slowpitch. Our rules clearly state a runner is out when he leaves the field of play. This is a question about the letter of the rule versus the intent of the rule.

One of our fields has a chain link fence running from the backstop to approximately 20' past the first base. The fence ends there, and a very clearly marked white line extends from that point on, marking the field of play.

Batter/runner hits a solid single, overruns first base, is safe, and decelerates without making any move toward second. The problem is, and I've never seen this before, his deceleration is the longest I've ever seen. I am standing there watching him slow to an amble at an angle towards the out of play line. As I said, the chain link fence extends at least 20' past first base and is at least 15' away from the baseline. I'm not watching in anticipation of a "gotcha" moment. It's more like I'm watching in disbelief, thinking, "Is he really going to slow to a crawl and then walk out of bounds?" Sure enough, he did, stepping both feet over the line, then turning and heading back towards first.

Now what do I do? Is he out for leaving the field of play? Or is the intent of the rule to put finality to a play when a runner, thinking he or she is out, leaves the field and heads to the bench?