What’s not accurate? When I read “a black hole”, I don’t assume we’re talking about Sagittarius A*, just a black hole.
For the sun we suppose the person speaking knows of THE Sun. For the supermassive black hole at the center of the galaxy we don't.
This can be easily shown as "The Black Hole Threw a Star Out of the Milky Way Galaxy" is clearly misusing the definite article.
Agree that _just_ an article swap leaves the headline worse off.
Anyway there’s only one sun and many black holes.