But the exit code can't change from 0 to 1. For any given input to the Unix program, if the output was 0 with one implementation, then it would always remain 0

But the exit code can't change from 0 to 1. For any given input to the Unix program, if the output was 0 with one implementation, then it would always remain 0 with any other _equivalent_ implementation. This is literally what is meant by "returns the same values for the same arguments". Any function that fits this description, by definition, cannot suffer from the problem you are describing.