First, the DC voltage of these fans is a separate voltage system from the AC/mains of the house.

Whether the 12v comes from a transformer or a switching power supply, the DC and AC circuits are effectively separated by that device.

The ground of the 12v system exists only within that system (and is provided by the transformer/power supply).

Consider the tranformer/power supply to be a battery with a positive and negative terminal. Inside, a chemical reaction will take place that moves electrons from one set of plates to another, leaving “holes” in one set, and extra electrons on the other.

This creates an imbalance - an electrical potential - and entropy says everything should try to balance. So those extra electrons provide the voltage, and once a circuit is made, will immediately try to balance the potential by moving through the circuit to the other terminal.

Using a transformer/power supply provides those electrons (and a sink - somewhere for those electrons to return to) from AC/mains voltage.

This is a pretty simple way to view it, there are more details that an EE would take me to task for, but it’s a good starting point.