Replacing a diy'd light fixture
In answer to your question. Yes it is acceptable to connect your light fixture the same way. Line to red. White or neutral to white, and ground or bare to ground. Ground wires do not normally carry current unless there is a fault event, and can be run exposed. Best description is that are like an electrical safety valve, they are a secondary source to return a complete a fault back to the over current protection that prevents users from an electrical shock or burn hazard.