Not sure i fully follow.
However that was just a basic conceptual example its a bit worse.
Not only can the uv of points 2 and 3 represent the right two vertices of quad1 and conversely represent the left two vertices of quad 2.
When you extend this to a center quad in a grid mesh its 4 vertices each connect to 4 quads. And a quad can share its vertices with 8 other quads each with its own unique uv requirements.