Isn't copying someone else's blog content to your own site copyright infringement? Couldn't the author of the content send Feedly a DMCA takedown notice?
Note - I love feedly, and, with the exception of HN, NYT, xkcd and twitter, it's where I consume all my content from the web. This was just a misstep, and I'm sure they'll do the right thing.
Feedly and other news reader services have de facto permission to gather blog posts at the request of users and then show them to those users. This is a half step beyond that, so you can't really call it copyright infringement.