The thing to remember with voltage is that it's not an absolute value. It's the difference between potentials at two different points in the circuit - that is why it is also sometimes called potential difference.

Your \ is the the potential difference between that point and ground. Sometimes that will be small, such as the voltage drop across a diode (when an input is LOW). Other times it will be large, governed by the current flow through the load and the pullup resistor.

\ can never be 0V in your example circuit simply because the lowest it can be is the voltage drop across a diode. For a normal silicon diode that is around 0.7V. The only way you could get \ to be 0V would be to connect it directly to ground bypassing the diode. It is then 0V WRT ground because it is itself ground.

The datasheet gives an example.

By adjusting the pot we can null any offset error. An offset error is when the inputs are exactly equal but the output isn't exactly zero. This error is also characterized by the datasheet:

It can be safely ignored in AC applications, where this offset will be ignored by the AC coupling. It becomes more important in DC applications, especially amplifiers, since this DC error will be amplified by the next stage.

This offset voltage exists because a real omp-amp can't be ideal. There will always be some unintended asymmetries between due to random variation in manufacturing. In all cases, there are op-amp designs that can minimize these errors, but usually at the expense of some other parameter, like cost.