How does an LED matrix work?
In your actual circuit, have you connected the wires and the LED leads at the junctions indicated by the black circles, or have you connected them wherever the lines overlap in your schematic diagram?

The correct reading of the schematic is to only have connections where indicated by the junction indicators (black filled circles). If you do so, then the third scenario in your diagram does not exist - the wires going horizontally and vertically do not actually touch at all.

One way to visualize this: The horizontal wires are all on the plane of your work table, the vertical wires are all in a plane floating an inch above the table, and the LEDs are the only connections between these two sets, and the only connections are the black circles.

You are correct, electricity will follow a path of least resistance to the greatest extent. In the schematic, there is no path of least resistance, i.e. short-circuit, between row and column wires, since no junctions are indicated. If you have interconnected the row and column wires, disconnect them now. Then, as you will see, the only path that allows electricity flow is through the respective diode / LED.