Hi Vincent -
When you try to split the patch with the cube-object, you will notice that it fails. That is because the edges of the cube are not within tolerance of the patch surface. When you then force a split with those edges, they have to somehow be pulled to the patch surface, and, in this case, that produces a trim curve that is rather unlike the input.
The better way to deal with this is to untrim the surfaces of the cube and use those surfaces that cleanly intersect the patch surface to trim the patch.