Does a 12 V battery system need to be earthed?

It depends on the installation, and the answer is set by the applicable regulations rather than by the voltage. A vehicle bonds the negative to the chassis by design; a boat, a shed and a house each follow different rules, and an inverter’s output side is a separate question again.

This page will not give a wiring diagram, because earthing is the one topic on this shelf where the right answer is genuinely different in each setting.

Why the low voltage does not settle it

The battery side may be low voltage, but the same installation usually contains an inverter producing mains-style voltage, and a charger connected to a building supply. Earthing decisions on the low-voltage side interact with both.

What a vehicle does by default

Road vehicles bond the battery negative to the chassis and use the chassis as a return path. That is a design decision made by the vehicle manufacturer, and additions are expected to respect it rather than introduce a second reference.

What changes elsewhere

Boats, static installations, sheds and houses each have their own applicable standards, and they differ on whether and where a bond is made. A generator has its own requirement again, documented in its manual, and it is one of the instructions most often skipped.

Why residual-current protection depends on it

A residual-current device works by detecting an imbalance that has to have somewhere to go. Whether it functions on an inverter’s output depends on how that output is referenced, which is why the inverter’s documentation covers it explicitly and why it is worth reading before rather than after.