Why does getppid() still return old parent pid after setsid()?

I've tried this code on both MacOS and Linux yet the child process getppid()
still returns its original parent process instead of "1" for init which is
what I'd expect. Isn't setsid() supposed to completely detach the child or
have I misunderstood?

int main()
{
        printf("Parent pid %d\n",getpid());
        switch(fork())
        {
        case -1:
                perror("fork");
                return 0;
        case 0:
                // child
                break;
        default:
                // Parent
                sleep(1);
                return 0;
        }

        setsid();
        printf("Child parent = %d\n",getppid());
        return 0;
}