This is, to some extent, what all news organizations do. Even the AP, those tiny local paper-reading-then-rewriting scamps! Much of newsgathering consists of reading all your competitors' stories and going from there. If you can't think of a new angle on the story, it's called "following up," usually with no credit given; if you can find a new angle, it's considered a totally new story, definitely without credit given.
Obviously you can't let some crappy knockoff copy and paste your stories and present them as their own (this happens to us sometimes!). But recognize this is much more about the letter of the law than the spirit of it. All journalism outfits are thieves! Just tell people where you stole your stuff from. How hard is that? [This story we stole from THR, Esq]