Found the bug. The problem is when the camera position is set after the ArcballControls is created. In the official example, one just need to move camera.position.set() after arcballGui.setArcballControls(). The fix is easy, because it is just a question of calling controls.setCamera(camera) again.
arcballGui.setArcballControls();
camera.position.set(0, 0, perspectiveDistance); <---- moved here
controls.setCamera(camera); <----- fix
Nonetheless, this caused the problem with mobile devices, because
nearPos0 becomes less than zero, in ArcballControls.js:
this._nearPos0 = camera.position.distanceTo( this.target ) - camera.near;
I do not think Ricardo will see this post, but maybe it helps someone else in the future…