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we will write the copy displayed on our site for our feed and then link it to the site where the article actually resides...
ie CNN has a breaking news story in an area that our site specializes in, can we just link to them through our feed using their paraphrased info as the header or do we need their permission to do so?
Does this also apply to podcast? or can we just link to them on our site?
If your RSS feed links to your own page, which summarizes the news story, it should be ok as long as you don't directly quote more than a snippet of the news site's copyrighted content, provide attribution, and link to the original page. This is very commonly done -- and encouraging links is in fact why many publishers provide RSS feeds.
To be fully legal, you need to check the terms and conditions for the RSS feed, which are probably linked from the page listing the RSS feeds.