I have an iPhone 4 (A1349), updated to iOS 7.1.2. I synch on a McBook Pro.
My issue is that I have unchecked
synch podcasts in iTunes, and yet podcasts are still listed on the phone's
Podcasts app. I have tried both to uncheck
Sync Podcasts in iTunes and to keep it checked but to uncheck the
Automatically include ... box. In both cases the podcast app still lists the podcasts I subscribe to, and some episodes under those folders. The episodes listed include cloud as well as downloaded episodes. The episodes are playable. An example of such a podcast is
Freakonomics Radio, but all my subscriptions are listed.