Models can be completely visible (i.e. not affected by the near clipping plane) in the MeshLab view, but then when you do "Save snapshot", the front vertices of the model will be black, i.e. clipped by the near plane in the saved snapshot. When you then move the near-plane closer to the camera, which moves the near plane back in the main view, the saved snapshot becomes even more clipped by the near plane.
On the other hand, when you move the near plane forward, so the mesh becomes nearly wholly occluded in the 3D view, then the saved snapshot will fully render and not be clipped anymore.
I think there is a bug here with rendering and the near value.