No, that's incorrect. Not the absolute closest no matter what. The closest points directly along the Y-axis so that if you subtracted that distance the triangles would touch.
That's the problem. Most triangle-triangle tests (Moller, Eberly) are simply seeking intersection (there is no intersection!). I want the distance that brings them into primary 'intersection'. In a non-time dependent scenario, one could just check a very fine resolution grid of points over the two triangles to find the shortest distance (a scan-line approach). When you want to find this before the end of time (because there are literally tens of thousands of triangles to test) you must consider optimal situations. The situation is that the edge segments of each side of each triangle checked against the edge segments of the other is the current popular method - but even as complex as this is, it yields the absolutely shortest distance indifferent to the direction of this distance vector. In reality, say one triangle completely enveloped by the other from an X-Z plane projection, one must do both segment-segment and segment-triangle tests. And I only want to consider the shortest distance in one direction.
For example, you have two complex polygon objects, one above the other, and you want the one above to move so as to be just touching the other. Not polyhedrons, not planes, any polygon objects. One must get down to considering polygon-polygon - in my case triangle-triangle - distances to do this. Think placing a set of polygon-object trees (hovering above) onto a polygon-object landscape accurately. Currently, I do ray-triangle intersection testing where the source triangle's vertices are the start of the ray directed -Y towards the target triangle. This is good in many situations but doesn't cover all cases (where none of the source/target triangle vertices are actually over the target/source triangle even though the two triangles obviously intersect).