Relay module for dummies

Chagrin:
There's no need to connect the Arduino GND to the GND of the module

Agree

Chagrin:
...and doing so will negate the optical isolation.

This is what I don't really understand. Why would it negate the isolation? AFAIK when a second source is provided, the Arduino's Vcc is only used for the octocoupler, so why would it hurt having a common ground?