As much as I like to make fun of TLS for all their shananagins, I agree 100 percent that they are not allowed to publish a story that contains lashon harah. The "Chilul Hashem" story doesn't hold any water if they are violating halacha, and there is zero heter of parnassah in lashon harah. (The Chofetz Chaim famously writes that if a boss tells you that if you don't say lashon harah he will fire you, and you will have no other source of parnassah, you are still not allowed to say the lashon harah.)
If one cannot get around the issue of lashon harah, they should close down their site.
And there is nothing wrong with being a blog site and not an "unbiased, we publish everything" news site.