If you check 'Bounds' in the Object tab > Viewport Display panel to help you spot it, and hit
AltH in Edit Mode to unhide all elements, the hidden vertex is revealed..

Edit (Better understanding of OP)

If you show the internal triangulation for rendering by using a Wireframe node, you can see that the (non-planar) quads are indeed triangulated in opposite directions:

..(and here the shipped add-on Measureit has been used to show vertex indices at a reasonable size.)

I've found that can be flipped by CtrlT manually triangulating with a real, editable edge, selecting the appropriate direction, 'Fixed' for 1st and 3rd vertices, 'Fixed Alternate' for 2nd and 4th:

Then CtrlX Limited Dissolving the new edge, setting the angle high enough to lose it:

After that, the internal triangulation appears to follow the hint:

.. and you get good ol' Z-fighting between the coincident faces, which is what you would expect.