I'm trying to find an algorithm to find the distance between a line-segment and an OOBB. I have an algo that I don't really understand that's implemented in JiglibX. The problem with this algo is that when the line intersects the box on two points, the returned position cannot be trusted (I need the point closest to the segment origin).

I would use GJK first and if this returns a penetration you could use SAT to find the MPD.