Just wondering about something. please see the first comment.
I'd have to see some evidence of this; a scientific study. For the sake of argument, I'll assume you're right, they cross perpendicular. Maybe it isn't what they see, but what they feel on the edge of the road, both on their feet and drag on their shell, that orientates them. It could be an instinctual orientation maneuver in order to overcome obstacles in nature.
I had a friend years ago whose office overlooked a parking lot that was partway gravel. Being the obsessive personality that he was he wondered about people's paths when they walked across it. He even ended up filming some to analyse.
He demonstrated (informally of course) that people unconsciously tended to follow Snell's Law -- the same path light takes entering or leaving a transparent object. That path also happens to be the timewise(not necessarily lengtwise) shortest distance between two places.
Life can be surprisingly elegant the way it optimizes situations for things like, say, the convenience or safety of turtles.