Why is the Digital 0 not 0V in computer systems?

You are getting confused. Look at TTL for example: -

enter image description here

A low input level is between 0 volts and some small value above 0 volts (0.8 volts for the case of TTL).

why do we take the trouble to set the 'low' to any positive voltage at all?

We take the trouble to ensure it is below a certain small value.

Picture from here.

You are confusing the "ideal" value with the valid input range.

In usual logic, in ideal conditions, the logical zero would be precisely 0V. However, nothing is perfect in real world, and an electronic output has a certain tolerance. The real output voltage depends on the quality of wires, EMI noise, current it needs to supply etc. To accommodate these imperfections, the logic inputs treat a whole range of voltage as 0 (or 1). See the picture in Andy's answer.

What your lecturer probably meant by 0.75V is one of the points making the logical 0 range.

Note there is also an empty range between 0 and 1. If the input voltage falls here, the input circuit cannot guarantee proper operation, so this area is said to be forbidden.

It is impossible to produce true zero volts logic signalling. There must be some tolerance allowed for, as the circuitry is not infinitely perfect. Spending money trying to make it infinitely perfect would not be a good investment of design funds either. Digital circuitry has proliferated and advanced so fast because its uses huge numbers of copies of the very simple and tolerant circuits that are logic gates.

The binary states 1 and 0 are represented in digital logic circuits by logic high and logic low voltages respectively. The voltages representing logic high and logic low fall into pre-defined and pre-agreed ranges for the logic family in use.

The ability to work with voltages within these ranges is one of the primary advantages of digital logic circuitry - it's not a failing. Logic gate inputs can easily distinguish between logic high and logic low voltages. Logic gate outputs will produce valid logic high and low voltages. Small signal noise is removed as logic signals pass through gates. Each output is restoring the input signal to a good logic voltage.

With analogue circuits, it is between more difficult and practically impossible to distinguish noise from the signal of interest and to reject the noise entirely.