Breeding true... means... Say you take a black lab and another black lab and breed them... you know your going to get black lab puppies. They're a breed, and breeding them together always gets the same result. This is breeding true... true to the breed standard.
Now take a black lab and breed it to a poodle. You get a labradoodle... which is a first generation hybrid. If I take another labradoodle and breed it to the first, a whole myriad of possibilities happens. You could have some straight coated dogs, some could be curly, some could be a mix of that... So, a labradoodle doesn't breed true.
So same here, your sex link has a fun name, like a labradoodle, but it doesn't mean its a breed. Its a hybrid that won't breed an expected result each time. You can recreate it, but you won't always get the same result.
And again, the green sheen is just what happens on black feathers. My flock has some black hens and they sheen green as well. Not a male trait.