It's either center, or the ship is placed in the actual physical center of the mesh.
The center of the physical mesh seems to be where it defaults to. However, I remembered the Advent frigate factory definitely does not build ships in the center of the mesh, and I found this which was not in my list of valid meshpoints.
Position [ 0.000000 147.216888 0.000000 ]
[ 1.000000 0.000000 0.000000 ]
[ 0.000000 1.000000 0.000000 ]
[ 0.000000 0.000000 1.000000 ]
Going to try this and hope it lets me move the point.
Edit: Yup, the game will use ShipBuild if present in the model, and if not will default to the center of the mesh (where the faction icon is displayed). If you see this Myfist you might want to make a note on your site as this isn't mentioned in the modeling documentation.
Edit2: You can also apparently change the orientation of this meshpoint and the ship will be rotated accordingly.