And they have these recommended connection configurations for bypass capacitors placement relative to the bypassed component:
The first case where both the component and the capacitor are on the same side I think I understand why the component's and capacitor's connections to power plane 2 are closely spaced. This should be to minimize the inductance of the component's power pin's connection to the bypass capacitor. And this low inductance is important for supplying the component's internal as well as I/O current surge demands.
But I'm not getting the reasoning for the second case with the component and capacitor on the opposite sides of the board. Why is this different connection configuration needed? It seems this adds extra distance for the currents to travel increasing inductance. Why wouldn't one connect the adjacent pins of the capacitor and component to the same power plane?